Speakers

Joseph M. Abdou

Paris 1 and PSE

The structure of board games

We introduce a variant of extensive games called board games. In the standard extensive model (Kuhn model) a game is described by a rooted tree. The position of the player determines the history. A board game is described by a rooted directed acyclic graph. A position may have multiple histories. Any board game can be represented by a strategically equivalent standard game (of imperfect information) such that on each information set the future potential plays do not depend on the actual position in that information set. This motivates the introduction of the class of extensive games with effective perfect information. We study rectangularity of strategic game forms associated to board game forms. We prove that any board game form is interactively equivalent to some standard extensive game form of perfect information and - strangely enough - it may fail to be strategically equivalent to that extensive game form.

Ethem Akyol

The Pennsylvania State University

Welfare Comparison of School Choice Mechanisms under Incomplete Information

We compare two widely used allocation methods for school choice, the Deferred Acceptance (DA) mechanism and the Boston mechanism, in terms of welfare. We consider a symmetric incomplete information setting in which students have (cardinal) valuations for schools and schools have identical preferences/priorities over students. Our main result is that when the number of schools and students is large, every type of student prefers the Boston mechanism to the DA mechanism. Although this strong result is not true when the number of schools is small, even in this case, the Boston mechanism is ex-ante welfare superior to the DA mechanism under weak conditions on the distribution of valuations.

Abhinav Anand

Stony Brook University

Quotas versus Handicaps: A Game Theoretic Analysis of Armative Action Policies in India

We analyze the affirmative action policy implemented in India, the Quota Policy, in which preference is given to the disadvantaged section of the populace by reserving a certain fraction of positions for them. We compare it to a hypothetical policy called the \Handicap Policy" in which the performance index of the disadvantaged is given an artificial boost instead, by means of an additive handicap. We conclude that on many important metrics of performance of affirmative action policies, Quotas and Handicaps can be shown to be equivalent to each other.

Guy Arie

University of Rochester

Dynamic Costs and Moral Hazard: A Duality Based Approach

The marginal cost of effort often increases as effort is exerted. In a dynamic moral hazard setting, dynamically increasing cost create information assymetry that breaks the sufficiency of one-shot-deviation incentive compatibility (OSD-IC), preventing any analysis. This paper recovers OSD-IC and characterizes the optimal contract. The result is obtained by developing an alternative formulation for dynamic moral hazard that is based on duality theory. The stronger result utilizes a critical feature of the new formulation -- a history's value is monotonic in the dual state space and satisfies a single crossing condition. The optimal contract is consistent with the popular yet thus far puzzling use of non-linear incentives, for example in salesforce compensation.

Robert John Aumann

Hebrew University of Jerusalem

Collectives as Individuals

In many applications of Game Theory, a player is a collective such as a household, team, political party, country or the like. Usually, this is understood as an idealization. In games where, say, countries are modeled as players, the "real" players are the individual citizens, with their individual goals and individual decisions and individual free will. It's only because this "true" game is too big and unwieldy to analyze that, it is held, game theorists model players as they do.

Here, we advance the thesis that it *IS* really that way: that in large part, collectives are like individual people, and may be thought of as such. And, perhaps, not only in Game Theory.

Yu Awaya

Penn State University

Communication in a Dynamic Prisoner's Dilemma with Incomplete Information

This paper provides a model in which communication is necessary in order to achieve cooperative outcomes in a long-term relationship. The model is a dynamic prisoner's dilemma with incomplete information about payoff s. The payoff s are private information and stochastically evolve over time. I study two situations. In one, players play simultaneously in every stage, knowing their own types. In the other, players exchange cheap talk messages after knowing their own types but prior to play. I show that there exists a nearly efficient payoff vector that is achieved as an equilibrium outcome when communication is possible and players are patient, but cannot be achieved without communication no matter how patient the players are.

Yaron Azrieli

The Ohio State University

The optimal sovereignty partition

(Joint work with Dan Levin)

A society faces a binary decision problem, say whether death penalty should be legalized or not. Agents' utilities have both common and private values components: The common value corresponds to whether legalizing death penalty reduces crime, and the private component corresponds to each agent's personal attitude towards executions. In the ex-ante stage, before types are realized, the society may split into smaller groups (states, provinces, etc.), such that each group makes its own decision about the issue. We analyze the optimal number of groups to which the society should split, when the objective is to maximize equilibrium welfare. Two competing forces determine the optimal partition: Larger groups aggregate information better and increase the common value utility for all agents, while smaller group can ``tailor'' the decision to their own private values.

Brian Baisa

Yale

Auction Design without Quasilinear Preferences

I analyze auction design in a private value setting where I remove the standard restriction that bidders’ preferences are linear in money. Instead, I only assume that bidders’ have positive wealth effects and declining marginal utility of money. While most research in auction design restricts bidders’ preferences to be quasilinear, there are many economic environments in which this restriction is violated. I show that removing the quasilinearity restriction leads to qualitatively different solutions to the auction design problem whether we are concerned with efficiency or revenue maximization. On efficiency, I show that probabilistic allocations of the good can Pareto dominate the second price auction; and there is no symmetric mechanism that is both Pareto efficient and dominant-strategy implementable. On revenue, I construct a probability demand mechanism with greater expected revenues than standard auction formats when there are sufficiently many bidders.

Barna Bako

MTA TKI

Exclusive contracts with product differentiation in successive oligopolies

(Joint work with Marco Haan)

This paper investigates the incentives of manufacturers to deal exclusively with retailers in bilaterally oligopolistic industries with brand differentiation by manufacturers. With highly differentiated products exclusive contracts are shown to generate higher profits for symmetric manufacturers, who thus have an incentive to insist on exclusive contracting. However, if the products are close substitutes no exclusivity will emerge in equilibrium. By introducing asymmetric upstream firms we find that the cost effective manufacturers offer unilaterally exclusive contracts to retailers when product differentiation is moderate

Andrei Barbos

University of South Florida

Project Screening with Tiered Evaluation

We study a Bayesian game of two-sided incomplete information in which an agent, who owns a project of unknown quality, considers proposing it to an evaluator, who has the choice of whether or not to accept it. There exist two distinct tiers of evaluation that differ in the benefits they deliver to the agent upon acceptance of a project. The agent has to select the tier to which the project is submitted for review. Making a proposal incurs a cost on the agent in the form of a submission cost. We examine the effect of changes in the payoff parameters at the two tiers of evaluation on the efficiency of the equilibrium outcome. We show that changes in these parameters that are aimed at increasing the level of self-screening exerted by the agent do not necessarily have beneficial effects either on the quality of projects submitted for review or on the quality of projects that are implemented. From a methodological viewpoint, our paper proposes a novel method of performing comparative statics in games whose equilibria are defined by a system of equations with no closed-form solution.

Alex Barrachina

University Carlos III de Madrid

Entry with Two Correlated Signals

(Joint work with Yair Tauman and Amparo Urbano)

We analyze industrial espionage extending the Milgrom and Roberts (1982) (hereafter MR) model. More precisely, we consider the case where a monopoly (M) is engaged in R&D trying to reduce his cost of production and deter a potential entrant (E) from entering the market. The R&D project may be successful or not and its outcome is a private information of M. The entrant has an access to an IS of a certain precision that generates a noisy signal on the outcome of the R&D project, and she decides whether or not to enter the market based on two signals: the price charged by M and the signal sent by the IS. It is assumed that the precision of the IS is exogenous and common knowledge.
We show that the separating equilibria of our model coincide with that of MR. The same result is obtained for pooling equilibria if the precision of the IS is sufficiently low to affect the decision of E of staying out. For the other extreme, if the IS is very accurate, then contrary to the MR model, pooling equilibrium does not exist. For intermediate values of the precision, the set of pooling equilibria is non-empty and E enters if the IS tells her the R&D project was not successful. Since in the MR model the entrant never enters in a pooling equilibrium, we show that the use of the IS by the potential entrant with high probability increases competition in pooling equilibrium.

Juan Ignacio Block

Washington University in St. Louis

Codes of Conduct and Bad Reputation

We study bad reputation games from the perspective of self-referentiality. In self-referential games players have the possibility of understanding opponents' intentions, and this can mitigate the problem of bad reputation. We characterize the probabilities of the Stackelberg type required to overcome a bad reputation problem when there is a possibility that intentions can be observed directly. The complementarity between direct and indirect observation of opponents' intentions is shown to be qualitatively different from games where all agents are long-lived.

Steven Brams

New York University

Inducible Games: Using Tit-for-Tat to Stabilize Outcomes

(Joint work with Steven J. Brams and D. Marc Kilgour)

Assume that one player (A) in a two-person game can probabilistically detect the strategy choice of its opponent (B) in advance, and that this fact is known to both players. We say that A adopts probabilistic tit-for-tat if it credibly commits to cooperating if B does, otherwise not, as signaled by its imperfect detector. In 20 of the 57 distinct 2 2 strict ordinal games with no mutually best outcome (35 percent), probabilistic tit-for-tat induces a non-Nash, Pareto-optimal outcome that is favorable to A. We call such games inducible. Sometimes the inducement is “weak,” but more often it is “strong.” As a case study, we consider the current conflict between Israel and Iran over Iran’s possible development of nuclear weapons and show that Israel’s credible commitment to probabilistic tit-for-tat can, with sufficiently accurate intelligence, induce a cooperative choice by Iran in one but not the other of the two plausible games that we argue model this conflict.

Philip N. Brown

The University of Colorado at Boulder

Social Coordination in Unknown Price-Sensitive Populations

(Joint work with Philip N. Brown, Jason R. Marden)

In this paper, we investigate the relationship between uncertainty and a designer’s ability to influence social behavior. Pigovian taxes are a common approach to social coordination. However, guaranteeing efficient behavior typically requires that the system designer has complete knowledge of the user population’s sensitivity to taxation. In this paper, we explore the effect of relaxing this requirement in the context of congestion games with affine costs. Focusing on the class of scaled Pigovian taxes, we derive the optimal tolling scheme that minimizes the worst-case efficiency loss under uncertainty in user sensitivity. Furthermore, we derive explicit bounds which highlight how the level of uncertainty in sensitivity degrades performance.

Brandon Jonathan Campbell

Texas A&M University

Theory on the Design of Experiments.

An experiment is a structured model to measure the validity of a hypothesis. There is extensive literature on how to design an experiment, derived by taking a already run experiment as a starting point, and determining what could be done better to get results that are more conclusive. As a result, the concept of an experiment has been treated informally, but if we seek to design an experiment, we need a formal basis. This paper formalizes the concept of an experiment, and what it means to test a hypothesis. It defines what an experiment is, what a hypothesis is, it defines the concept of construct validity, which is similar to identification or internal validity, and establishes basic experimental design features necessary to get conclusive results. Future work on this paper will consider the case where not everything is controllable, and we have to test things indirectly.

Evangelia Chalioti

University of Illinois at Urbana-Champaign

Team members' ability matters for career concerns

This paper studies career concerns in teams when the support a worker receives depends on the quality of the team she belongs to - the effort and ability of her fellow team members. It argues that implicit incentives to work and help arise. By exerting effort and providing support, a worker influences her own and colleague's performances and thus, can effectively bias the learning process in her favor. Each agent enjoys a reputational bonus equal to the total rents generated by her activity. Intensified dependence among team members also increases the returns of supplying labor and thus, implicit incentives. This paper also argues that, if explicit contracts are provided, reputation and sabotage-like incentives arise.

XiaoGang Che

University of Alberta, Canada

Entry Deterrence in Dynamic Second-Price Auctions

(Joint work with XiaoGang Che, Tilman Klumpp)

We examine a dynamic second-price auction with sequential and costly entry. We show that collusive equilibria exist in which placing a low early bid has a signaling effect that deters entry by subsequent bidders. As a result, fewer bidders enter on expectation, and the bidders who do enter obtain a higher expected payoff in equilibrium, compared to the benchmark equilibrium where all bidders immediately submit their true values. A special case of an entry-deterring equilibrium is one with incremental bidding, where, after having submitted low opening bids, buyers raise their bids by small amounts in each period. Computations show that the social effect of collusion is primarily a transfer from the seller to the buyers, while efficiency losses are relatively small.

Yu Chen

Indiana University

Centralization or Decentralization in Multi-Agency Contracting Games?

I explore whether two major contracting procedures, decentralized menu design and centralized mechanism design, are strategically equivalent in multi-agency contracting games. Unlike single-agency, multi-agency suggests strategic behaviors of the agents and the interrelated impacts of different agents' asymmetric information on the principal's objective. I find that centralization can take advantage of joint-base mechanisms, as a useful communication device related to relative information evaluation, to better deal with the interrelated information asymmetry in general multi-agency games with ex post implementation. Technically, my main contribution is to show that ex post menu design is merely strategically equivalent to individual-based ex post mechanism design rather than joint-based ex post mechanism design, which actually makes the principal better off than the former two. My findings support the rationale of centralized economics design and associated information communication from another perspective. I also apply the main results to incentive-based financial regulation with interrelated banks, and discuss why the regulatory contracting cannot be decentralized without loss of generality.

Onur Cobanli

Humboldt University Berlin

Pipeline Power

(Joint work with Prof. Franz Hubert)

Using the Shapley Value we analyze the impact of three controversial pipeline projects on the power structure in the Eurasian trade of natural gas. Two of them, Nord Stream and South Stream, allow Russian gas to bypass transit countries, Ukraine and Belarus. Nord Stream’s strategic value turns out to be huge, justifying the high investment cost for Germany and Russia. The additional leverage obtained through South Stream, in contrast, appears small. The third project, Nabucco, has received strong support from the EU Commission. It aims at diversifying Europe’s gas imports by accessing producers in Middle East and Central Asia. Nabucco curtails Russia’s power, but the benefits accrue mainly to Turkey, while the gains for the EU members are negligible.

Daniel Cracau

University of Magdeburg

Firm behaviour in price-quantity oligopolies: An experimental study of the mixed strategy equilibrium

(Joint work with Benjamin Franz (University of Oxford))

We study oligopoly games with firms competing in prices and quantities simultaneously. We systematically compare our experimental results to the theoretical predictions using the mixed strategy equilibria for linear demand functions. Subjects' price choices are mainly between marginal cost and monopoly level but do not follow the equilibrium distribution. Although average prices and profits are above theoretical values, we do not observe a high level of collusion as expected in the literature. By comparing simulations based on the mixed strategy equilibrium to our experimental outcomes, we conclude that in this game price setting can be explained by strategic reaction to preceding round results. In contrast to the equilibrium prediction, we observe a decrease in prices and negative average profits for the triopoly game.

Nuh Aygun Dalkiran

Bilkent University

Common Knowledge and State-dependent Equilibria

(Joint work with Moshe Hoffman, Ramamohan Paturi, Daniel Ricketts, Andrea Vattani)

Many puzzling social behaviors, such as avoiding eye contact, using innuendos, and insignificant events that trigger revolutions, seem to relate to common knowledge and coordination, but the exact relationship has yet to be formalized. Herein, we present such a formalization. We state necessary and sufficient conditions for what we call state-dependent equilibria – equilibria where players play different strategies in different states of the world. In particular, if everybody behaves a certain way (e.g. does not revolt) in the usual state of the world, then in order for players to be able to behave a different way (e.g. revolt) in another state of the world, it is both necessary and sufficient for it to be common p-believed that it is not the usual state of the world, where common p-belief is a relaxation of common knowledge introduced by Monderer and Samet (1989). Our framework applies to many player quorum games – a generalization of coordination games that we introduce – and r-common p-beliefs – a generalization of common p-beliefs that we introduce. We then apply these theorems to three particular signaling structures to obtain novel results. Finally, as a by-product, we resolve some of the outstanding puzzles.

Geoffroy De Clippel

Brown University

On the Selection of Arbitrators

(Joint work with Kfir Eliaz and Brian Knight)

A key feature of arbitration is the possibility for conflicting parties to partake in the selection of the person who will rule the case. We analyze this problem of the selection of arbitrators from the perspective of implementation theory. Theoretical, empirical and experimental arguments are combined to highlight difficulties with a procedure that is commonly used in practice and to develop and identify better performing procedures.

Rahul Deb

University of Toronto

Implementation with Securities

(Joint work with Debasis Mishra)

We study mechanism design in a setting where agents know their types but are uncertain about the utility from any alternative. The final realized utilities are observed by not only the agents but also the mechanism designer and can be contracted upon. In such environments, the mechanism designer is not restricted to use only transfers but can use security contracts, which depend on both the announced types and the realized utilities. We show that using security contracts instead of transfers expands the set of (dominant strategy) implementable social choice functions. Our main result is that in a finite type space, every social choice function that can be implemented using a security contract can also be implemented using a royalty contract. Royalty contracts are simpler security contracts, where the agent initially pays a transfer and keeps a fraction of the realized utility depending on his announced type. We also identify a condition called acyclicity that is necessary and sufficient for implementation in these environments.

Amrita Dhillon

University of Warwick

Status incentives and corruption

(Joint work with Antonio Nicolo)

We re-examine the hypothesis that increasing compensation to public sector officials reduces corruption, defined as bribe-taking. We introduce heterogeneity among agents on the dimension of how much they are motivated by "status" or prestige of a profession vs purely monetary compensation. We show that increasing wages in this setting may increase corruption under realistic conditions on parameters. Using "prestige" as a choice variable for policy may have reinforcing effects in reducing corruption: it reduces both bribe taking behaviour as well as improves the selection of workers in the public sector. Media, on the other hand, by emphasising the "bad news" about corruption may worsen corruption reducing the status of a profession. Finally, we show that in our setting the use of non-monetary bonus, like medals, may improve both the the quality of the officials and their honesty.

Lu Dong

University of Nottingham

Trying to Overcome Coordination Failure in a Tough Environment

(Joint work with Lu Dong; Maria Montero; Alex Possajennikov)

Using experimental methods, this paper investigates whether leadership can be successful in overcoming a history of coordination failure in a tough environment. The environment is a weak-link game in which a player's payoff is positively related to the minimum effort in the group and negatively related to his own effort. All players exerting a high effort is the payoff dominant Nash equilibrium, but the parameters are such that the benefits of coordination are low compared to the cost of mis-coordination. Given this tough environment, play converges to the most inefficient equilibrium in the initial phase of the experiment. We then explore whether the introduction of a leader would help the group to climb out of the coordination trap. We consider two types of leader: a cheap talk leader who suggests an effort level, and a first mover whose choice of effort is observed by the rest of the group. We use the strategy method to measure the responsiveness of the followers, and we also elicit the leader's beliefs about the followers' response. Some leaders exhibit strategic teaching behaviour, and most followers are quite responsive towards the leader's choice. The first mover treatment has a higher proportion of matching strategies, in which followers replicate the leader’s choice. However, no group escapes the coordination trap, due to some leaders choosing the lowest effort or due to a minority of followers who chose the lowest effort in response to any choice of the leader. Leadership changes the behaviour of some players in the short run but has little effect on the minimum group effort in both short and long run.

Songzi Du

Simon Fraser University

Ex Post Equilibria in Double Auctions of Divisible Assets

(Joint work with Haoxiang Zhu)

We characterize ex post equilibria in uniform-price double auctions of divisible assets. Bidders receive private signals and inventories, have interdependent and linearly decreasing marginal values, and bid with demand schedules. In a static double auction we characterize a linear ex post equilibrium, in which no bidder would deviate from his strategy even if he would observe the signals and inventories of other bidders. Moreover, under certain conditions this ex post equilibrium is unique. In a dynamic market with a sequence of double auctions and stochastic arrivals of new signals, we characterize a dynamic ex post equilibrium, whose allocation path converges exponentially in time to the efficient level. We demonstrate that the socially optimal trading frequency depends on the arrival process of new information. Our ex post equilibrium aggregates dispersed private information and is robust to distributional assumptions and details of market design.

Umut Dur

University of Texas at Austin

Sequential Assignment Problems and Two Applications

(Joint work with Onur Kesten)

We study matching markets from practice, where a set of objects are assigned to a set of agents in two-steps. The placement of students to the exam and mainstream public schools in the U.S. and the appointment of teachers to the public schools in Turkey until recently are two examples of such markets. We analyze the mechanisms currently in use in both markets and show that they fail to satisfy desirable fairness and welfare criteria. Moreover, they give participants perverse incentives: misreporting preferences can be beneficial and improved performance on admission test may worsen the assignment of a participant. We characterize the subgame perfect Nash equilibria of the induced preference revelation games in both markets which motivate us to propose an alternative method, applicable to both markets, through which assignments take place in a single step. This may also help explain why Turkish ministry of education abandoned their two-step assignment system.

Omer Edhan

The University of Manchester

Cost Sharing with Production Constraints

Two common assumptions in many works on cost sharing are 1. the lack of reciprocal production constraints; namely, it is assumed that if a bundle is to be produced then any ``smaller" bundle can be produced, and 2. the cost function is differentiable. This is obviously not the case in many cost problems of interest. Haimanko (2002) addressed the second matter, but not the first, and his methods may not be extended to treat the first matter. We consider two classes of cost problemד whose sets of producible bundles are centrally symmetric convex bodies, and whose cost functions have (generically) major non-differentiabilities. The cost functions in the first class are convex exhibiting non-decreasing marginal costs to scale, and those in the second class are piece-wise linear. We show existence and uniqueness of a cost allocation mechanism, satisfying standard axioms, on these classes.

Lorini Emiliano

IRIT-CNRS

When the Group Matters: A Game-Theoretic Analysis of Team Reasoning and Social Ties

(Joint work with Frederic Moisan)

In this paper, we investigate a central theory from the economics literature whose aim is to clarify how agents reason and are able to cooperate when acting as members of the same group: Bacharach's theory of team reasoning. After discussing the various limitations of this theory in modeling various types of social interactions, we introduce a new model of social ties which appears to provide a simpler and more intuitive approach to modeling collaborative actions in the context of complex strategic games where competing groups may coexist. We illustrate the advantage of this model by performing a detailed comparative analysis of both theories.

János Flesch

Maastricht University

Refinements of subgame-perfect epsilon-equilibrium in games with perfect information

We consider games with perfect information and deterministic transitions. A common solution concept is the concept of subgame-perfect epsilon-equilibrium, where epsilon>=0, which is a strategy profile such that no player can improve his payoff in any subgame by more than epsilon. We propose and examine a number of refinements of this concept. A major emphasis lies on existence results. Roughly speaking, the most important refinements require the following respective properties: (1) no player makes a big mistake with positive probability, (2) the mistakes vanish as the horizon approaches infinity, i.e. epsilon depends on the subgame and goes to 0 as play proceeds, and (3) for pure strategy profiles, the induced play paths are continuity points of the payoff functions.

Based on the joint papers:
-- Flesch J, Kuipers J, Mashiah-Yaakovi A, Schoenmakers G, Shmaya E, Solan E and Vrieze K [2013]: Equilibrium refinements in perfect information games with infinite horizon. Working paper.
-- Flesch J and Predtetchinski A [2013]: Subgame-perfect epsilon-equilibrium with vanishing errors. Working paper.

Francoise Forges

Universite Paris Dauphine

Bayesian repeated games

(Joint work with Antoine Salomon)

We consider Bayesian games, with independent private values, in which uniform punishment strategies are available. We establish that the Nash equilibria of the Bayesian infinitely repeated game without discounting are payoff equivalent to tractable separating (i.e., completely revealing) equilibria and can be achieved as interim cooperative solutions of the initial Bayesian game. We also show, on a public good example, that the set of Nash equilibrium payoffs of the undiscounted game can be empty, while limit Nash equilibrium payoffs of the discounted game, as players become infinitely patient, do exist.

Drew Fudenberg

Harvard University

Recursive Stochastic Choice

We characterize two sorts of stochastic choice rules in which the agent makes current decisions using a forward-looking value function that takes future randomizations into account. Both sorts of rules generalize logistic choice, and are equivalent to it in static problems. The rules differ in how the agent views future choice sets and how he views his future randomizations. One rule is equivalent to the discounted logit used in applied work, and exhibits a "preference for flexibility;" the other is "error-averse" and penalizes the addition of undesirable choices to a menu.

Alexander Funcke

Stockholm University

Making empathy obsolete: Enforcing equilibrium selection despite path-dependency

A main results from epistemic game theory is that for games with multiple reasonable equilibria the predictive devil really is in the details, and may hinge on the exact type of belief revision employed, the players’ initial belief distributions and to what extent they are common knowledge. Changing perspective from the theorist to the real world insight implies that for a large class of games we can not predict outcomes.

In this paper we are interested in how much a principal would need to alter the specifics of a multiple equilibria game (keeping labels intact) to instill a shift from one equilibrium to another. A mechanism design-like approach is taken, where a principal prefer that the agents in a population play a certain strategy. Every agents’ strategy choice will depend on an unknown, the ratio of choosing the principal’s preferred strategy. It is shown that with the introduction of a system of fines and rewards where the sizes are a function of an approximation of the same ratio can be tweaked such that the problem gets epistemically reduced from a complex to a trivial one, by making empathy obsolete. That is to make the player’s decision independent of the choices of the others and doing so without any new transfers (in equilibrium). Lastly, conventions and by extension norms are explored in relation to this mechanisms e.g. as ways to instill norm change.

Bernhard Ganglmair

University of Texas at Dallas

Conversation with Secrets

(Joint work with Emanuele Tarantino)

We analyze the sustainability of a conversation when one agent might be endowed with a piece of private information that affects the payoff distribution to its benefit. Such a secret can compromise the sustainability of conversation. Even without an obligation, the secret holder will disclose its secret if it prevents preemptive termination of the conversation. The non-secret holder lacks this possibility and stops the conversation. Competition and limited effectiveness of the conversation amplify this result of early disclosure and render the conversation process less sustainable. We discuss policy and managerial implications for industry standard development and joint ventures.

Bernhard Ganglmair

University of Texas at Dallas

Framing Games: Evidence-Based Decision Making in an Adversarial Setting

(Joint work with Luke Froeb and Steven Tschantz)

We study framing in an adversarial setting by turning the scientific process upside down. Instead of objective truth seekers who formulate hypotheses and then gather evidence to test them, we introduce a class of games between self-interested parties who frame existing evidence to influence a decision maker. The decision maker chooses between the frames based on the likelihood of each, which allows us to characterize the equilibrium decision as a statistical estimator. We find that the estimator is generally biased, and the bias favors the party with the more extreme claim. However, the bias disappears as the amount of evidence grows, and for certain classes of distributions, this kind of adversarial framing performs better than objective inquiry.

Daniel Ferguson Garrett

Toulouse School of Economics

Competitive Screening and Search

(Joint work with Renato Gomes and Lucas Maestri)

We study the steady-state equilibrium of a matching market with adverse selection in which privately informed agents are matched with new principals over time. Agents can only accept offers from principals with whom they are matched. Equilibrium offers are menus which screen agent information. While principals are ex-ante identical, the menus offered in equilibrium are dispersed. We derive the equilibrium distribution over menus. Menus are ordered so that "more generous" menus leave more surplus uniformly over agent types. More generous contracts are found to be more efficient.

Boris Ginzburg

University College London

Collective Preference for Ignorance

A committee needs to decide whether to approve a proposal. If approved, the proposal will give every member of the committee a private payoff, which can take different values depending on the state of the world. Before deciding on the proposal, the committee chooses whether to acquire a signal about the state. Even though information is costless, the choice is not always positive. I show that the the committee will decide to remain uninformed if and only if different realisations of the signal lead to the same collective decision; I also formulate a corresponding condition on the distribution of individual payoffs. The paper also shows that a rule requiring a larger plurality of voters to adopt a proposal becomes optimal as the ratio of potential individual gains to losses moves away from one in either direction.

Maria Goltsman

University of Western Ontario

On the optimality of diverse expert panels in persuasion games

(Joint work with Sourav Bhattacharya, University of Pittsburgh; Arijit Mukherjee, Michigan State University)

We examine a game where multiple senders communicate with a single uninformed receiver. Before the communication takes place, each of the senders, with a certain probability, learns the realization of the state of nature, which is a real-valued random variable. The information about the state is verifiable, so the senders cannot misrepresent it, but can conceal it by pretending they are uninformed. Upon seeing the senders’ messages, the receiver can take an action that affects the payoffs of all parties. The receiver wants his action to match the state of nature, whereas for each of the senders, the preferred action is state independent.

In this setting, we ask whether the receiver would prefer the panel of senders to include senders with identical or diverse preferences over the actions. Casual intuition suggests that a diverse panel should result in more informative communication: whenever one of the senders would prefer to conceal the information, a sender with the opposite interests would prefer to reveal it. However, we prove that under certain reasonable conditions on the receiver’s payoffs and the distribution of the state, the optimal sender panel is homogeneous: that is, all senders who are included in the panel have the same preferred action, equal to one of the endpoints of the interval over which the state is distributed. We investigate the conditions under which the optimal panel is homogeneous or heterogeneous, and test the robustness of the results to correlation in senders’ information and the possibility of costly information acquisition by the senders.

Renato Gomes

Toulouse School of Economics

Experimentation and Project Selection: Screening and Learning

(Joint work with Lucas Maestri (Toulouse) and Daniel Gottlieb (UPenn))

We study optimal contracting in a setting that combines experimentation and adverse selection. In our leading example, an entrepreneur (agent) is better informed than the investor (principal) about both the quality the project (risky arm’s distribution) and the entrepreneur’s outside option (payoff of the safe arm). The investor’s profit-maximizing mechanism can be uniquely implemented with a menu of equity contracts with different provisions on control rights. In each of these contracts, the investor offers a fixed initial payment (seed money) in exchange for a fixed share of the total revenue (equity), and a termination clause that specifies the critical number of failures before the project is aborted. We obtain necessary and sufficient conditions for the investor to extract all the rents from the entrepreneur’s expertise on project quality. Our model has implications for the design of contracts to finance innovative activities.

Ragavendran Gopalakrishnan

California Institute of Technology

Potential games are necessary to ensure pure Nash equilibria in cost sharing games

(Joint work with Jason R. Marden, Adam Wierman)

We consider the problem of designing distribution rules to share 'welfare' (cost or revenue) among individually strategic agents. There are many known distribution rules that guarantee the existence of a (pure) Nash equilibrium in this setting, e.g., the Shapley value and its weighted variants; however, a characterization of the space of distribution rules that guarantee the existence of a Nash equilibrium is unknown. Our work provides an exact characterization of this space for a specific class of scalable and separable games, which includes a variety of applications such as facility location, routing, network formation, and coverage games. Given arbitrary local welfare functions W, we prove that a distribution rule guarantees equilibrium existence for all games (i.e., all possible sets of resources, agent action sets, etc.) if and only if it is equivalent to a generalized weighted Shapley value on some 'ground' welfare functions W', which can be distinct from W. However, if budget-balance is required in addition to the existence of a Nash equilibrium, then W' must be the same as W. We also provide an alternate characterization of this space in terms of 'generalized' marginal contributions, which is more appealing from the point of view of computational tractability. A possibly surprising consequence of our result is that, in order to guarantee equilibrium existence in all games with any fixed local welfare functions, it is necessary to work within the class of potential games.

Olivier Gossner

Paris School of Economics & London School of Economics

The Appeal of Information Transactions

(Joint work with Antonio Cabrales and Roberto Serrano)

An information transaction entails the purchase of information. Formally, it consists of an information structure together with a price. We develop an index of the appeal of information transactions, which is derived as a dual to the agent's preferences for information. The index of information transactions has a simple analytic characterization in terms of a formula that depends on the relative entropy from priors to posteriors. That formula strikingly relates to free energy in theoretical physics. The index also connects naturally with a recent index of riskiness.

Yingni Guo

Yale University

Optimal Delegation Contract with Experimentation

This paper combines a principal-agent model and experimentation to study the following question: what is the optimal contract if experimentation can be delegated to a biased yet better informed agent while monetary transfers are not allowed? The principal owns a two-armed bandit whose risky arm might yield payoffs after exponentially distributed random times and the agent has private information regarding the risky arm’s quality. The optimal delegation contract is computed by a new method using optimal control and utilizes information of the learning process to minimize agency cost. Since a pessimistic agent values experimentation relatively less than an optimistic agent does and hence attaches more importance to exploiting successes, a self-claimed optimistic agent is asked to experiment for a long time and, if necessary, not allowed to cash in success immediately. This in turn provides incentives for a pessimistic agent to be honest.

Sergiu Hart

Hebrew University of Jerusalem

Two(!) Good To Be True

How to sell goods optimally? While the mechanism-design literature has solved this problem neatly when there is only one good, the multiple goods case turns out to be extremely difficult, mathematically and conceptually. Much of what is true for one good does not extend to multiple goods. We will try to explain the difficulties, show what can go wrong, and then present some universal approximation results. The talk is essentially self-contained; no background in mechanism design is necessary.

Sander Heinsalu

Yale

Continuous time noisy signalling

Most real-life signalling a la Spence 1973 is noisy and in many cases signalling takes time. This paper formulates the classic signalling model in continuous time, with Brownian noise obscuring the signal. Adding noise removes the need for belief-based equilibrium refinements, since any signalling level observed by the receiver is on the equilibrium path. The model allows for equilibria where signalling occurs in multiple disjoint intervals of beliefs. There may be no `most informative' equilibrium with a signalling region containing the signalling regions of all other equilibria. A noisier signal or a less patient sender shrinks the largest range of beliefs for which signalling can be sustained. If the bad type finds signalling sufficiently costly, then the set of equilibria shrinks as the noise increases or patience decreases. Patience and signal precision are interchangeable, as in the previous literature. The bad type prefers the pooling equilibrium, more so when there is little noise or the signaller is patient. The good type may prefer pooling or separating, with separating relatively better under more patience and less noise.

Ziv Hellman

Tel Aviv University

Spectral Value for Coalitional Games

(Joint work with Mikel Alvarez-Mozos, Eyal Winter)

Assuming a ‘spectrum’ or ordering of the players of a coalitional game, as in a political spectrum in a parliamentary situation, we consider a variation of the Shapley value in which coalitions may only be formed if they are connected with respect to the spectrum. This results in a naturally asymmetric power index in which positioning along the spectrum is critical. We present both a characterisation of this value by means of properties and combinatoric formulae for calculating it. In simple majority games, the greatest power accrues to 'moderate' players who are located neither at the extremes of the spectrum nor in its centre. In supermajority games, power increasingly accrues towards the extremes, and in unaninimity games all power is held by the players at the extreme of the spectrum.

Ed Hopkins

Edinburgh University

Inequality and Risk Taking Behavior

This paper investigates social influences on attitudes to risk and offers an evolutionary explanation of risk-taking by young low-ranked males. Becker, Murphy and Werning (2005) found that individuals about to participate in a status tournament may take fair gambles even though they are risk averse in both wealth and status. Here their model is generalized by use of the insight of Hopkins and Kornienko (2010) that in a tournament or status competition one can consider equality in terms of the status or rewards available as well as in initial endowments. While Becker et al. found that risk-taking is increasing in the equality of initial endowments, it is found here that it is increasing in the inequality of social rewards in the tournament. Further, it is shown that the poorest will be risk loving if the lowest level of status awarded is sufficiently low. Thus, the disadvantaged in society rationally engage in risky behavior when social rewards are sufficiently unequal.

Johannes Horner

Yale University

Truthful Equilibria in Dynamic Bayesian Games

(Joint work with Satoru Takahashi and Nicolas Vieille)

This paper characterizes an equilibrium payoff subset for Markovian games with private information as discounting vanishes. Monitoring might be imperfect, transitions depend on actions, types correlated or not, values private or interdependent. It focuses on equilibria in which players report their information truthfully. This characterization generalizes those for repeated games, and reduces to a collection of one-shot Bayesian games with transfers. With independent private values, the restriction to truthful equilibria is shown to be without loss, except for individual rationality; in the case of correlated types, results from static mechanism design can be applied, resulting in a folk theorem.

Chih-Ru Hsiao

Soochow University

A Geometric Interpretation of the Shapley value for TU Games

(Joint work with Wen-Lin Chiou)

We give the Shapley value of a TU game a new geometric interpretation
even if the core of the game is empty. We propose a new class of TU games, called coalitional regular in average games, abbreviated as CRIA games. A proper game is not necessary a CRIA game, neither is the converse, however, there are games which are both proper and CRIA. In the investigation of the solutions of a CRIA game, by observing the structure of the core of a game, we introduce the concepts of k-th semi-cores and k-th quasi-cores of an n-person game, for k=1, 2,…, n-1. When all quasi-cores of an n-person TU game are non-empty, enlightened by the concept of compromise, a middle way between two extremes, we propose the compromise solution of the TU game as the geometric centroid of the n-1 mass centers of the quasi-cores of the game. Surprisingly, we find that the compromise solution is exactly the Shapley value. This gives the Shapley value a new geometric interpretation and a new characterization, or say, a new intuitive interpretation, as the compromise solution.

Elena Inarra

University of the Basque Country

The von Neumann-Morgenstern Stable Sets for 2x2 games

(Joint work with C. Larrea, A. Saracho)

We analyze the von Neumann and Morgenstern stable sets for the mixed extension of 2x2 games when only single profitable deviations are allowed. We show that the games without a strict Nash equilibrium have a unique vN&M stable set and otherwise they have an infinite number of these sets. Moreover the unique vN&M stable set includes a Pareto optimal strategy profile.

Karl Robert L. Jandoc

University of Hawai'i

Stable Coalitions with Power Accumulation

(Joint work with Ruben Juarez)

Agents endowed with power compete for a divisible resource by forming coalitions with other agents. The coalitions with the largest power wins the resource and divide it between its members. We study four models of coalition formation where agents might or might not accumulate power and agents might or might not participate in further coalition formation processes. An axiomatic approach is provided by focusing in variations of two main axioms: self-enforcement, which requires that no further deviation happens after a coalition has formed, and rationality which requires that players pick the coalition that gives them their highest payoff. For four different cases, we determine existence of stable coalitions that are self-enforcing and rational for different sharing rules. The stable coalitions found for the cases can be implemented as subgame perfect Nash Equilibrium.

Zhengjia Jiang

 

The Lobbying Game with Asymmetric Information

The lobbying game is a constant-sum Colonel Blotto game with two distinguishing features -- the victor of each battlefield is determined probabilistically and payoffs are assigned discretely from the set {win, draw, loss}. At the heart of every lobbying game is the legislative body that the players are lobbying. Its members form a voting system, often one that is weighted. In this scenario, given specifics about the weighted voting system, it is possible to determine the equilibrium strategy that is optimal for both players. However, if one player lacks this information while his adversary possesses it, then a situation of asymmetric information is created. The disadvantaged player must necessarily deviate from the equilibrium strategy. This paper will argue that if the disadvantaged player has knowledge about the ramifications of deviating from the equilibrium strategy in each of the possible distinct weighted voting systems that may arise in the legislature, then he can treat his situation like a game against nature. Three strategy choices will be recommended, and a two-case example using a three-party legislature will be presented. In this way, the player without complete information will be able to exercise some control over his payoff.

Alfi Jiménez

Universidad Distrital Francisco José de Caldas

The Dark Side of Clientelism

(Joint work with Andrés Cendales)

This article analyzes, at a subnational level, a political system in which a precarious democracy takes shape once the mayor, as a member of a political organization constituting a political patronage machine, not only co-opts civil society but also seeks to plunder municipal funds to reinforce its political hegemony, weakening and even destroying the existing institutional framework. In direct contradiction to the central theses of economic voting and orthodox political economy, the main finding of this article demonstrates that the executive, through his local power networks operating in the context of a deteriorated social structure, do not promote processes of equitable wealth redistribution but instead promotes local empowerment processes through clientelist practices, creating a cartel government made up of the parties represented on the municipal council. The council, as a veto player, will strengthen and support the establishment of a predator state led by the executive.

J. Stephen Judd

U. Penn CIS

Conflict Begets Cooperation in Socialized KingPawn

We report experiments on a two-person game in which human subjects continuously choose to play either a dominant role (called a King) or a submissive one (called a Pawn). A King receives a higher payoff rate, but only if the partner is a Pawn. Straightforward equilibrium analysis predicts there will be no conflict (time when both players are Kings), but the behavioral data is utterly at odds with that, as is intuition.

We decompose the game into parts and offer an analytic solution for an important subgame. This yields a much more satisfying prediction of conflict behavior, and indeed the recorded games are extremely well correlated with the prediction. Both the theory and the data show structure in conflict that unequivocally encourages cooperative sharing behavior.

Ehud Kalai

Northwestern University

Compressed Equilibrium in Large Repeated Games of Incomplete Information

(Joint work with Eran Shmaya)

Due to their many applications, large Bayesian games have been a subject of growing interest in game theory and related fields. But to a large extent, models (1) have been restricted to one-shot interaction, (2) are based on an assumption that player types are independent and (3) assume that the number of players is known.

The current paper develops a general theory of Bayesian repeated large games that avoids some of these difficulties. To make the analysis more robust, it develops a concept of compressed equilibrium which is applicable to a general class of Bayesian repeated large anonymous games.

Jae Kang

University of Pittsburgh

Multiple Experts Informing a Constrained Decision-maker

This paper studies how constraints on a decision-maker impede information transmission from multiple experts who share the same preferences with the decision-maker. The experts have no ex-ante conflicts of interests with each other since they can only observe some dimensions of a state where they are interested in and have their own areas of expertise. However, the constraints create strategic tensions hindering revelation of information that would otherwise be completely transmitted. I characterize (informative) prefect Bayesian equilibria under various forms of the constraints. First, I identify the extent of the constraints to which full information revelation is possible. Second, I show that there exist partially revealing equilibria irrespective of the constraint level. Finally, I analyze the effect of the constraint level on social welfare. Counterintuitively, the less binding constraints do not necessarily guarantee Pareto-superior outcomes.

Dominik Karos

Saarland University

Power and Bargaining

We introduce a new power con figuration which takes into account bargaining between players within in coalitions. We show that under very weak conditions on a bargaining solution there is a power confi guration which is stable with respect to renegotiations. We further show that given this power con figuration there is a coalition which is both internally and individually stable. Finally we consider two diff erent bargaining solutions on apex games and show under which conditions there are core stable coalitions.

Eiichiro Kazumori

SUNY at Buffalo

Information Aggregation in Double Auction Markets with Interdependent Values

This paper considers uniform price double auctions among buyers and sellers with interdependent values and identifies conditions that equilibrium prices aggregate information as the market becomes large. When buyers and sellers have unit demand and supply, one dimensional signals and symmetric distribution of information, if their values have strict private value effects and the distribution of signals satisfies the strict monotone likelihood ratio property, then, every perfect equilibrium converges to an ex post equilibrium in the double auction game in the limit economy and equilibrium prices provide a consistent and asymptotically normal estimator of the fundamental value of the asset. In complex economic environments with heterogeneous distributions of signals, multidimensional signals, and multiple units of demand and supply, stronger private value effects and the strict monotone likelihood ratio properties are necessary to ensure information aggregation. Without these conditions, equilibrium prices in the limit economy can only be partially revealing.

SunTak Kim

National Taiwan University

Information Acquisition and Voting Mechanisms

(Joint work with John Duffy; Sourav Bhattacharya)

This study investigates the properties of optimal voting mechanisms, defined by group size and voting rule, with endogenous information acquisition. The standard model of jury voting with exogenous information predicts that the efficiency of group decision increases unambiguously with group size. However, once information acquisition becomes a costly decision, there is an important free-riding consideration that counterbalances the information aggregation effect. Since information is costly and acquired information is a public good, rational voters will purchase information with a lower frequency. An implication of the trade-off between information aggregation and free-riding is that there exists an optimal group size for a given voting rule. We thus compare the efficiency of group decisions under different group sizes to test whether we can observe significant decreases in both information acquisition and efficiency as the group size moves from the optimal size to a larger group size. We also consider the optimality of voting rules with a fixed group size. If information is exogenous, then there exists an optimal voting rule that achieves the highest efficiency and this rule can be different from majority rule with asymmetry in the precision of signals. This difference in efficiency of group decision can be more prominent under costly information as the optimal rule provides significantly greater incentives to acquire information than suboptimal rules.

Jin Yeub Kim

The University of Chicago

Endogenous Choice of a Mediator

In many economic and political situations, two parties in conflict often get stuck with a "bad" mediator. Despite a significant amount of the theoretical work on mediation, the theory of how mediators are chosen is not sufficiently understood. My interest is in understanding how the parties bargain over the choice of a mediator. My main insight is that a mediator is endogenously selected badly for "signaling" reasons. That is, since the parties do not want to reveal weakness, they choose the one who mediates in a way that is better for the strong type of both parties; and thus, a mediator with high probability of failure making peaceful settlement is chosen, which, in fact is war-durable and (interim but) not ex ante incentive efficient. In this sense, I argue that the very process of selecting a mediator itself create inefficiencies and show a common equilibrium feature of distortions. In this paper, I utilize the solution and refinement concepts in Holmström and Myerson (1983) and Myerson (1984) and build a cooperative bargaining theory foundation to a non cooperative signaling game.

Sofya Kiselgof

NRU Higher School of Economics

Matching with interval order preferences:stability and Pareto-efficiency

In this paper we analyse an extension of the classical Gale-Shapley two-sided matching model. There are colleges, that may admit no more than the quota of applicants and the applicants, each of whom is admitted to at most one college. Each side has preferences over the agents on the other side, and preferences of the colleges are considered to be the interval orders. We show that in this model a stable matching always exists. Furthermore, we prove that the Erdil-Ergin stable improvement cycle procedure is applicable in this case. So in this model it is possible to construct a mechanism, which finds a stable and Pareto-efficient matching. Unfortunately, above mentioned stable mechanism is not strategy-proof. We also provide a strategy-proof applicant-proposing deferred acceptance with tie-breaking. Novel special tie-breaking procedure leads to lower chances of an applicant-inefficient stable matching (in comparison to those with random tie-breaking).

Elon Kohlberg

Harvard University

Shapley Value of Stochastic Games

(Joint work with Abraham Neyman)

Dávid Kopányi

University of Amsterdam, Tinbergen Institute

Price-Quantity Competition with Risk-averse Firms

We consider the market for a homogeneous good in which two firms simultaneously decide on both the price and the production level of the good. It is known from the literature that, under complete information and with profit-maximizing firms that are risk neutral, there exists no pure-strategy Nash equilibrium in this model (see e.g. Levitan and Shubik, 1978). In this paper we show that a Nash equilibrium in pure strategies may exist when firms are risk averse and hold noisy conjectures about the action of the other firm.

We calculate the Nash equilibrium in pure strategies numerically for the case where firms have mean-variance preferences and we analyze how this equilibrium depends on important parameters of the model such as the degree of risk aversion and the amount of uncertainty in the conjectures about the action of the other firm. Contrary to the mixed-strategy Nash equilibrium under risk neutrality and complete information, each firm now produces less than the market demand at the equilibrium price. Aggregate production, however, may be larger as well as smaller than the market demand, depending on the preferences and beliefs of the firms. We find that the more risk averse the firms are, the less they produce and the higher price they ask in equilibrium. Aggregate production exceeds market demand for low degrees of risk aversion and firms have some unsold products. As firms become more risk averse, aggregate production will not satisfy the demand in equilibrium. Thus, given the beliefs of firms, there exists an optimal level of risk aversion for which aggregate production equals equilibrium demand so no consumer or producer will be rationed.

Tatiana Kornienko

University of Edinburgh

A Cognitive Basis for Adaptive Utility

This paper provides a new approach to a utility function, by deriving it from deeper first principles. Using a minimum set of cognitive tools, one can evaluate choice options and their expectations using solely information from one's past and present environments. The adaptive evaluation procedure results in one's utility function being isomorphic to a perceived rank of its magnitude within a reference set, and thus provides a mechanism for one's attitudes towards risk to be shaped entirely by one's experiences, memory, and cognitive imperfections. The proposed parsimonious model links recent developments in economics, psychology, and neuroscience, and shows that environmental context, memory, and cognitive processes may interact in non-trivial and economically relevant ways.

Ernest Lai

Lehigh University

Eliciting Private Information with Noise: The Case of Randomized Response

This paper analyzes survey response with a game of information transmission. A respondent who is averse to lying and to being stigmatized responds to a question regarding his type. With or without knowing the question (respectively deterministic and randomized response), an interviewer updates beliefs after receiving the response. No information can be transmitted under deterministic response for low ratio of lying aversion to stigmatization aversion; informative equilibria exist under randomized response for any non-zero ratio. For low aversion ratio, a set of truthful equilibria under randomized response achieves the maximal mutual information allowed by any equilibrium; for high ratio, other informative equilibria, existed under both randomized and deterministic response, dominate the truthful equilibria and achieve the maximal mutual information. Subjects in experiments truthfully responded more often under randomized response. Truthful behavior under deterministic response exceeds equilibrium level. The mutual information implied by observed behavior is consequently higher under deterministic response.

Timothy Lambie-Hanson

Suffolk University

Shared Risk in n-player Games

(Joint work with Christopher Lambie-Hanson)

We analyze a game where the world is either in a good state or a state of disaster. We assume each player chooses an action in which her payoff in the good state of the world is increasing, but so is the probability of the bad state. After describing the conditions under which all pure strategy Nash Equilibria (PSNE) are symmetric and, alternatively, at most one symmetric PSNE exists, we show that if multiple PSNE exist (symmetric or otherwise), the least risky strategy profile is optimal among that set. However, no interior PSNE is socially optimal among all strategy profiles, as all interior PSNE are too risky.

Rida Laraki

CNRS and Ecole Polytechnique

Higher Order Game Dynamics

(Joint work with Panayotis Mertikopoulos)

Continuous-time game dynamics are typically first order systems where payoffs determine the growth rate of the players' strategy shares. In this paper, we investigate what happens beyond first order by viewing payoffs as higher order forces of change, specifying e.g. the acceleration of the players' evolution instead of its velocity (a viewpoint which emerges naturally when it comes to aggregating empirical data of past instances of play). To that end, we derive a wide class of higher order game dynamics, generalizing first order imitative dynamics, and, in particular, the replicator dynamics.

We show that strictly dominated strategies become extinct in n-th order payoff-monotonic dynamics $n$ orders as fast as in the corresponding first order dynamics; furthermore, in stark contrast to first order, weakly dominated strategies also become extinct for n>=2. All in all, higher order payoff-monotonic dynamics lead to the elimination of weakly dominated strategies, followed by the iterated deletion of strictly dominated strategies, thus providing a dynamic justification of the well-known epistemic rationalizability process of Dekel and Fudenberg (1990). Finally, we also establish a higher order analogue of the folk theorem and we show that convergence to strict equilibria in $n$-th order dynamics is n orders as fast as in first order.

Emiliya A Lazarova

University of Birmingham

Paths to stability in two-sided matching under uncertainty

(Joint work with Emiliya Lazarova and Dinko Dimitrov)

We consider one-to-one matching problems where individuals have preferences over the possible types of the agents on the opposite side of the market. Initially, players know the `name' but not the `type' of their potential partners. In this context learning occurs via matching and using Bayes' rule. Types are assigned to agents as random independent draws from the set of types without replacement. We introduce the notion of a stable and consistent outcome, and show how the interaction between blocking and learning behavior shapes the existence of paths to stability in such an environment. Existence of stable and consistent outcomes then follows as a side result.

Joosung Lee

Penn State University

Bargaining and Buyout

Extending the random-proposer model (Baron and Ferejohn, 1989; Okada, 2011) and the random-bilateral-meeting model (Gul, 1989), we introduce a non-cooperative coalitional bargaining model in which agents can strategically buy out other agents. With buyout options, due to agents’ strategic alliance behaviors, an efficient coalition may not be formed immediately in stationary subgame perfect equilibria and the equilibrium payoff vector is not necessarily in the core. We characterize conditions for a grand-coalition equilibrium and an efficient stationary equilibrium. Two applications are studied. For simple games with veto players, non-winning intermediate coalitions may be formed and the equilibrium winning coalition is not always minimal. For employer-employee games, workers form a union and the equilibrium wage is higher than the marginal product of each worker.

Yehuda Levy

Hebrew University

Stochastic Eventual Perfect Monitoring

(Joint work with Itai Arieli)

We study information structures in repeated interactions in which players learn about each others' actions via stochastic signals. We formulate a condition of eventual approximate learning of actions and states, and show that this condition can be reformulated using approximate mutual learning, using merging of conditional beliefs, or using orthogonality-preserving transition kernels from the action/state space to the signal space. Applications include determinacy of Borel games and learning correlated equilibrium in repeated games.

Yuke Li

Yale University

A Computational Model of Conflict and Cooperation

This paper considers the problem of 2-player conflict, which arises due to competition over resources. Each player represents a certain country and has some total resources/wealth. A player may either attack to get the resources or maintain peace. I present a computational game-theoretic model for such interaction between the players and show some key questions of interest to policy makers that can be answered efficiently. They are: (1) given the resources and the power of each player, is peace a stable situation? and (2) what can influence the likelihood of conflict? I propose one optimization algorithm to compute all the Nash Equilibria in the model and show that the peace efforts(negotiated settlements) may prove futile because one-sided defection is attractive. I also identify some material factors (size of the disputed item and the relative power e.g) and non-material factors(nationalism, audience costs, e.g) that can enter into the conflict/cooperation calculation and thereby influence the likelihood of conflict.

Fei Li

University of Pennsylvania

Revenue Management without Commitment: Dynamic Pricing and Periodic Fire Sales

(Joint work with Francesc Dilme)

We consider a market with a profit-maximizing monopolist seller who has K identical goods to sell before a deadline. At each date, the seller posts a price and the quantity available but cannot commit to future offers. Over time, potential buyers with different reservation values enter the market. Buyers strategically time their purchases, trading off (1) a possibly lower price in the future with the risk of being rationed and (2) the current price without competition. We analyze equilibrium price paths and buyers' purchase behavior. We show that incentive compatible price paths decline smoothly over the time period between sales and jump up immediately after a transaction. In equilibrium, high value buyers purchase immediately on arrival. Crucially, before the deadline, the seller may periodically liquidate part of his stock via a fire sale to secure a higher price in the future. Intuitively, these sales allow the seller to ‘commit’ to high prices going forward. The possibility of fire sales before the deadline implies that the allocation may be inefficient. The inefficiency arises from the scarce good being misallocated to low value buyers, rather than the withholding inefficiency that is normally seen with a monopolist seller.

Sina Litterscheid

University of Bonn

Sequential, multidimensional Screening

(Joint work with Dezsö Szalay)

We study a sequential screening problem where the agent produces multiple items and has a multidimensional type that he learns over time. With multiple payoff relevant parameters and action choices, the optimal contract does not necessarily induce truthtelling of equilibrium path. Instead, sequentially optimal lying strategies need to be discouraged. The resulting optimal mechanism displays nonstandard features such as upward distortions. We apply our results to the optimal timing of productive decisions; if postponing all production decisions is feasible, then it is always preferred unless the principal’s utility of consuming the goods is independent of the amount of other goods consumed.

Yan Liu

Stony Brook University

Bank Competition and Lending Policy over Business Cycles

(Joint work with Yan Liu)

Two facts of bank lending policy over business cycles, i.e., countercyclical loan spread and credit standard, are well documented in the empirical literature. Within a framework of dynamic credit market, featuring asymmetric information and imperfectly competitive banks with costly screening technology, it is showed analytically that the equilibrium (of a repeated game) captures simultaneously the two spects of bank lending policy. Furthermore, the equilibrium countercyclicality stems exclusively from time variation of competitive intensity among banks, which is supported specifically by an often overlooked evidence contained in Fed’s Senior Loan Officer Opinion Survey. More strikingly, when the basic framework is extended to account for variable funding cost, i.e., risk-free rate, then it can be showed that an extended period of historically low risk-free rate will induce excessively low credit standard, which provides an explanation for the unusual events in the credit market over years leading up to the Crisis.

Ting Liu

Stony Brook University

Reputation building in credence good markets

(Joint work with Yuk-fai Fong)

This paper studies reputation building in credence goods markets. Many professional services are credence goods because consumers lack the expertise to judge service qualities. For this reason, reputation plays an important role in the interaction between experts and clients. Yet, if consumers have difficulty to verify qualities of the services they have received, how is trust fostered and what is the mechanism that discipline experts? How does legal protection for consumers interact with experts’ incentives to maintain a good reputation?
In our model, a long-lived, risk-neutral expert encounters an infinite sequence of short-lived, risk-neutral consumers, each of whom needs a treatment to fix her problem. A consumer’s problem may cause a major or a minor loss, which can be prevented if the expert implements the appropriate treatments. We assume that it is efficient to have the problem fixed. The expert posts a price list at the beginning of each period. Then, a consumer arrives at the marketplace and consults the expert for appropriate treatments. After diagnosis, the expert learns the nature of the consumer’s problem. He either makes a recommendation from the posted price list or refuses to treat the consumer. At the end of the period, the expert’s price list, his recommendation, the consumer’s decision and her utility become public information.
There does not exist a fully-revealing equilibrium in which appropriate treatments are implemented. When the expert is impatient, the expert truthfully reveals the nature of consumers’ problems, but the major problem is left untreated with a positive probability. When the expert is sufficiently patient, appropriate treatments are implemented. Yet, the expert does not reveal any information about consumers’ problems. We find that contrary to the static model, legal protections for consumers may undermine the expert’s incentive to maintain a good reputation, hence reducing the efficiency of the market.

Heng Liu

University of Rochester

Efficient mechanism design in interdependent-valuation environments

In this paper, we provide a generic existence result for efficient mechanisms in dynamic interdependent valuation environments. We use the inter-temporal correlation of different agents' private information to construct a sequence of payment schedules under which truth-telling consists of an ex post equilibrium after all histories. While previous results in static mechanism design with interdependent valuations are mostly negative, we show that inter-temporal consideration can offer an easy and intuitive solution to efficient implementation.

Georgy Loginov

UW Madison

Cyclical Behavior in Two-Speed Evolutionary Game Environments

We present a model of two-speed evolution in a generalized coordination game, in which preferences slowly adjust to changes in the aggregate behavior of the population. Under best-response and replicator dynamics the unique steady state of joint dynamics of strategies and preferences is repelling. The same result holds for logit dynamics with small noise levels, whereas for large noises the steady state becomes a sink.

Shih En Lu

Simon Fraser University

Almost Fully Revealing Cheap Talk with Imperfectly Informed Senders

(Joint work with Attila Ambrus and Shih En Lu)

We show that in multi-sender communication games where senders imperfectly observe the state, if the state space is large enough, then there exist equilibria arbitrarily close to full revelation of the state as the noise in the senders' observations gets small. In the case of replacement noise, where the senders observe the true state with high probability, we show this in a game with one round of direct communication. In the case of continuous noise, where senders observe a signal distributed according to a continuous distribution over a small interval around the true state, we establish similar results for mediated communication, and (with more restrictions on the noise structure) for multiple rounds of direct communication. The results imply that when there are multiple experts from whom to solicit information, if the state space is large, then even when the state is observed imperfectly, there are communication equilibria that are strictly better for the principal than delegating the decision right to one of the experts.

Georgy Lukyanov

Toulouse School of Economics

Coordination Frictions and Public Communication

(Joint work with Tong Su)

Under global games' framework, we analyze the choice of information disclosure from a benevolent public agent (sender), who can send the message to a group of private players (receivers) before they take actions. It is shown that, in the presence of coordination frictions, conflict of interests arises endogenously. As a result, public information provision in equilibrium is coarse and presents partition structure. Interestingly, compared to benevolent public agent, introducing a small exogenous bias in the sender's preferences can mitigate the inefficient information provision problem and hence improve social welfare.

Jason Marden

University of Colorado at Boulder

Selecting Efficient Coarse Correlated Equilibria Through Distributed Learning

(Joint work with Jason R. Marden)

A learning rule is completely uncoupled if each players behavior is conditioned only on his own realized payoffs, and does not need to know the actions or payoffs of anyone else. We demonstrate a simple, completely uncoupled learning rule such that, in any finite normal form game with generic payoffs, the players realized strategies implements a Pareto optimal coarse correlated (Hannan) equilibrium a very high proportion of the time. A variant of the rule implements correlated equilibrium a very high proportion of the time.

Adrian Marple

Stanford University

Equilibria in Finite Games with Imperfect Recall

(Joint work with Adrian Marple and Yoav Shoham)

We generalize traditional equilibrium concepts for finite games in extensive form with behavioral strategies so that they apply to all games, including games of imperfect recall. Adapting and augmenting previous definitions (in particular, by Piccione and Rubinstein, and by Battigalli), we define four notions: Distributed Agent Equilibrium (DAE), Distributed Nash Equilibrium (DNE), Distributed Sequential Equilibrium (DSE), and Distributed Perfect Equilibrium (DPE). We show that, in a precise sense, these extend the classical equilibrium notions: (a) they form a strict inclusion hierarchy (e.g., every DNE is a DAE but not necessarily vice versa, and so on up the hierarchy), (b) every game has a DPE (and therefore also a DSE, DNE and DAE), and (c) in the subclass of games of perfect recall, DAE, DNE, DSE and DPE collapse, respectively, to agent equilibrium, Nash equilibrium, sequential equilibrium, and perfect equilibrium. In service of these results we introduce several novel notions -- including partial symmetry, the distributed agent form and phantom strategies -- which may be interesting in their own right.

Timothy Mathews

Kennesaw State University

A Sequential Choice Model of Family Business Succession

(Joint work with Tim Blumentritt)

A game theoretic model of family business succession, in which an elder sibling (E) and a younger sibling (Y) sequentially choose levels of pursuit for a managerial leadership position, is developed and analyzed. After observing chosen pursuit levels, the founder of the business selects a successor. Intuition suggests that E might enjoy a "first mover advantage." After determining a Subgame Perfect Nash Equilibrium for the specified sequential move game, the possibility of a "first mover advantage" is explored in two ways. First, direct comparisons of the equilibrium outcome are made between E and Y. It is argued that when E and Y have the same value for the position, E realizes a higher payoff than Y if and only if the founder is predisposed to choose E as the successor. Second, the potential for the sequential nature of the framework to systematically alter the payoff of a player in a particular direction is addressed by fixing the values of all relevant parameters in the model and making a comparison of a particular candidate’s equilibrium expected payoff if he is E versus if he is Y. This counterfactual exercise reveals that: (i) a candidate of fixed attributes always realizes a greater probability of being chosen as successor if he is E (instead of Y) and (ii) an individual prefers being E (over being Y) if and only if the value he places on being chosen as successor and/or the predisposition of the founder to choose him as successor are relatively low.

Alexander Matros

University of South Carolina

Common Value Mechanisms with Private Information

(Joint work with Alex Possajennikov)

Melayne McInnes

University of South Carolina

Lake Wobegon: Experimental Tests of Learning and the “Better than Average Effect”

(Joint work with Alexander Matros, Chun Hui Miao)

Garrison’s Keillor’s fictional town, where "all the women are strong, all the men are good looking, and all the children are above average," has been used to describe the illusory superiority phenomenon in which individual’s overestimate their capabilities relative to a population. The Lake Wobegone effect has been observed among drivers, CEOs, undergraduate and MBA students, and many other groups. In order to analyze this effect, we propose the following game. First, each of the n players is randomly assigned a number from 1 to n (without replacement). Then, each player has to make a choice between two actions: either to enter the contest, or not. Players who choose not to enter receive a fixed payment A > 0. Each entrant has a chance to win a prize. To be a winner in the contest, the entrant’s number must be above the average for all entrants. Each entrant with a number equal to or below the average gets 0. All the winners split the contest prize equally. Suppose that k players enter the contest. Then, the contest prize is equal to kA + B, where B, the jackpot “sweetener” is greater than zero. Efficiency requires that at least two players enter the contest when B > 0. However, the game is strictly dominance solvable with a unique Nash equilibrium in which no player will enter the contest. In the second part of our paper, we first test to see whether play converges to the predicted equilibrium in the lab. Next, we explore sensitivity to the parameter choices. Our game is related to well-studied p-beauty contests and the traveler’s dilemma, but there are three key differences: our game is strictly dominance solvable, asymmetric (each player draws a different number), and our strategy space is a simple enter/not enter decision rather than choosing a number in an interval. These differences allows us to measure how well the models developed to explain thinking and learning in the p-beauty contest and traveler’s dilemma explain behavior in a different environment

Zsombor Zoltan Meder

Maastricht University

Naiveté and sophistication in dynamic inconsistency

(Joint work with János Flesch, Ronald Peeters)

This paper introduces a general framework for dealing with dynamic inconsistency in the context of Markov decision problems. It carefully decouples concepts that are often entwined in the literature, distinguishing between the decision maker and its various temporal agents, and between the beliefs and intentions of the agents. Classical examples on naive and sophisticated decision makers are formalized and contrasted based on this new language. Providing a unified formalism to deal with these issues allows for the introduction of a mixed type of decision-maker, who is naive in some states and sophisticated in others. Such a mixed type can be used to model situations which were inaccessible to previous approaches.

Andrey Meshalkin

Maastricht University

Subgame Perfect Equilibria in Majoritarian Bargaining

(Joint work with P. Jean-Jacques Herings, Andrey Meshalkin, Arkadi Predtetchinski)

We study three-person bargaining games with discounting, where an alternative is accepted if it is approved by a majority of players. We characterize the set of subgame perfect equilibrium payoffs and show that for any proposal in the space of possible agreements there exists a discount factor such that given the proposal is made and accepted by one of the players in period zero. Also we construct a subgame perfect equilibrium such that arbitrary long delay of acceptance occurs with probability one.

Tomasz Michalak

University of Oxford

The Marginality Approach for the Shapley Value in Games with Externalities

(Joint work with Oskar Skibski and Michael Wooldridge)

One of the long-debated issues in coalitional game theory is how to extend the Shapley value to games with externalities (partition-function games). In particular, when externalities occur, a direct translation of Shapley's axioms does not imply a unique value. In this paper we study the marginality approach, based on the idea of an alpha-parametrized definition of the marginal contribution, where alpha is a vector of weights associated with an agent joining/leaving a coalition. We prove that all values that satisfy the direct translation of Shapley's axioms can be obtained using the marginality approach. Moreover, for every such value, there exists a simple strengthening of standard axioms that suffices to imply a unique value. Based on this, we turn our attention to the analysis how properties of a value translate to the requirements on the definition of the marginal contribution (i.e. weights alpha). Finally, we prove that under certain conditions, other axiomatizations of the Shapley value (Young's marginality axiomatization and Myerson's axiomatization based on the concept of balanced contributions) translated to games with externalities using the proper definition of the alpha-parametrised marginal contribution are equivalent to Shapley's axiomatization.

Alan Daniel Miller

University of Haifa

A Behavioral Arrow Theorem

(Joint work with Alan Miller and Shiran Rachmilevitch)

In light of research indicating that individual behavior may violate standard rationality assumptions, we introduce a model of preference aggregation in which neither individual nor collective preferences must satisfy transitivity or other coherence conditions. We introduce an ordinal rationality measure to compare preference relations in terms of their level of coherence. Using this measure, we introduce a new axiom, monotonicity, which requires the collective preference to become more rational when the individual preferences become more rational. We show that no collective choice rule satisfies monotonicity and the standard Arrovian assumptions: unrestricted domain, weak Pareto, independence of irrelevant alternatives, and nondictatorship.

Stefania Minardi

HEC Paris

Warm-Glow Giving and Freedom to be Selfish

(Joint work with Ozgur Evren)

Warm-glow refers to other-serving behavior that is valuable for the actor per se, apart from its social implications. We provide axiomatic foundations for warm-glow by viewing it as a form of preference for larger choice sets driven by one's desire to have freedom to act selfishly. Specifically, an individual who experiences warm-glow values the availability of selfish options even if she plans to act unselfishly. Briefly put, warm-glow necessitates free will. Our theory accommodates the empirical findings on motivation crowding out and provides clear-cut predictions for empirically distinguishing between warm-glow and other motivations for prosocial behavior, a task of obvious importance for policy. The choice behavior implied by our theory subsumes Riker and Ordeshook (1968) on voting and Andreoni (1990) on the provision of public goods.

Saeed Mohammadian Moghayer

University of Amsterdam, and TNO Delft

Stock-dependent discrete-time dynamic pollution games

(Joint work with Florian Wagener, Paolo Zeppini)

In this paper we address the dynamics of strategic actions in a pollution game model where the payoff matrix of the game depends endogenously on the accumulation or depletion of an environmental stock variable. Our model has the structure of a stock-dependent dynamic game, that is a game where the pay-offs to the players changes with the evolution of an external state variable, which in turn depends on the action of the players. More specifically, we analyse a two-player stock-dependent dynamic game in which the stage game is a normal form game with myopic players who use Markov stationary strategy, that is they play a stage game Nash equilibrium in each period. A dynamic consequence of stock-dependent payoffs on the strategies played is that the qualitative structure of the solution of the stock-dependent stage game might change as the stock variable evolves. Here we develop a method to study these qualitative changes and classify the possible economic outcomes. The method is applied to the discrete time dynamic ecological-economic interest conflicts in the lake pollution game.

Frederic Moisan

University of Toulouse

The Behavioral Effects of Social Ties: an Experimental Study

(Joint work with Giuseppe Attanasi, Astrid Hopfensitz, Emiliano Lorini, Frederic Moisan)

This paper focuses on studying the nature of social relationships (between, e.g., friends, family relatives, colleagues, class mates, teammates, etc...) as a possible explanation of human cooperative behavior. After providing a basic definition of social ties, which relies on social identity theory from social psychology, we introduce a novel theoretical model built upon the main hypothesis that such social relationships influence a player’s choice by modifying his preferences. In order to investigate this theory, we propose an empirical analysis of a new kind of two player game, which allows to disentangle predictions from theories based on self-interest, social preferences, and social ties. Through an in-subject experimental design, we compare interactions in the above game according to three different levels of social ties between players (i.e., weak, intermediate, strong). As a main result, we provide empirical evidence that strong social relationships indeed promote cooperation, which validates the proposed theoretical model of social ties while rejecting other relevant theories of social preferences (i.e., inequity aversion, fairness) as a possible interpretation.

Christoph Mueller

Carnegie Mellon University

Robust Implementation in Weakly Rationalizable Strategies

Weakly rationalizable implementation represents a generalization of robust implementation to dynamic mechanisms. It is so conservative that virtual implementation in weakly rationalizable strategies is characterized by the same conditions as robust virtual implementation by static mechanisms. We show that despite that, (exact) weakly rationalizable implementation is more permissive than (exact) robust implementation in general static mechanisms. We introduce a dynamic robust monotonicity condition that is weaker than Bergemann and Morris' (2011) robust monotonicity condition and prove that it is necessary, and together with weak extra assumptions sufficient for weakly rationalizable implementation in general dynamic mechanisms. We demonstrate that sometimes even weakly rationalizable implementation in finite dynamic mechanisms is more permissive than robust implementation in general static mechanisms.

Kota Murayama

Hitotsubashi University

Robust Predictions under Finite Depth of Reasoning

(Joint work with N/A)

This paper elucidates how predictions in finite depth of reasoning model, special cases of which include level-k and cognitive-hierarchy models are robust to the common knowledge assumption of level-0 types' actions. We examine whether an outside observer can ignore a slight violation of the common knowledge assumption when she knows which game players will play with high probability but, with small probability, she does not know and they will play different games with respect to payoff structure and actions of level-0 types. A sufficient condition is provided for a p-dominant cognitive equilibrium, which is a natural analogue of p-dominant action profile in the finite depth of reasoning model, being robust to incomplete information a la Kajii and Morris (1997). Under a certain condition on players' beliefs, we show that even a p-dominant cognitive equilibrium which does not satisfy their robustness condition can be robust. As a by-product, this result implies that the level-k model has the smallest set of robust equilibria, and the cognitive-hierarchy model has the largest regarding p-dominance.

Rosemarie Nagel

UPF Barcelona, now visiting NYU

The agencies method for coalition formation in experimental games

(Joint work with John Nash, Axel Ockenfels, Reinhard Selten, )

In society, power is often transferred to another person or group. A previous work studied the evolution of cooperation among robot players through a coalition formation game with a noncooperative procedure of acceptance of an agency of another player. Motivated by this previous work, we conduct a laboratory experiment on finitely repeated three-person coalition formation games. Human players with different strength according to the coalition payoffs can accept a transfer of power to another player, the agent, who then distributes the coalition payoffs. We find that the agencies method for coalition formation is quite successful in promoting efficiency. However, the agent faces a tension between short-term incentives of not equally distributing the coalition payoff and the long-term concern to keep cooperation going. In a given round, the strong player in our experiment often resolves this tension approximately in linewith the Shapley value and the nucleolus. Yet aggregated over all rounds, the payoff differences between players are rather small, and the equal division of payoffs predicts about 80% of all groups best. One reason is that the voting procedure appears to induce a balance of power, independent of the individual player’s strength: Selfish subjects tend to be voted out of their agency and are further disciplined by reciprocal behaviors.

Heinrich Harald Nax

PSE, Ecole Normale Superieure

Learning in a Black Box

(Joint work with M. Burton-Chellew, S. West, H.P. Young)

Many interactive environments can be represented as games, but they are so large and complex that individual players are in the dark about what others are doing and how their own payoff s are aff ected. This paper analyzes learning behavior in such `black box' environments, where players' only source of information is their own history of actions taken and payoff s received. Specifi cally we study repeated public goods games, where players must decide how much to contribute at each stage, but they do not know how much others have contributed or how others' contributions aff ect their own payoff s. We identify two key features of the players' learning dynamics. First, if a player's realized payo ff increases he is less inclined to change his strategy, whereas if his realized payoff decreases he is more inclined to change his strategy. Second, if increasing his own contribution results in higher payoff s he will tend to increase his contribution still further, whereas the reverse holds if an increase in contribution leads to lower payoff s. These two eff ects are clearly present when players have no information about the game; moreover they are still present even when players have full information. Convergence to Nash equilibrium occurs at about the same rate in both situations.

Abraham Neyman

Hebrew University of Jerusalem

Robust equilibria of continuous-time stochastic games

We study continuous-time stochastic games (with finitely many states and actions), the existence of their equilibria and in particular those that are robust to changes of players' evaluations of streams of payoffs.

We show that the stationary discounting game has a stationary equilibrium, the generalized (not necessarily stationary) discounting game has an epsilon equilibrium, and in both cases there are strategy profiles that are epsilon equilibrium in all the games with a sufficiently small perturbation of the discounting.

A limit point of generalized discounting need not be a classical generalized discounting as some of the ``mass'' may be pushed to infinity. We show that for every such limit point there is a strategy profile that is an epsilon equilibrium of all the games with generalized discounting that are sufficiently close to the limit point.

Vladyslav Nora

Université catholique de Louvain, CORE

Saddle Functions and Robust Sets of Equilibria

(Joint work with Hiroshi Uno)

This paper introduces games with a saddle function. A saddle function is a real-valued function on the set of action profiles such that there is a single minimizing player, for whom minimizing the function implies choosing her best response, and the other players are maximizing players, for whom maximizing the function implies choosing their best responses. We provide a sufficient condition for the robustness of sets of equilibria to incomplete information in the sense of Kajii and Morris (1997, Econometrica), Morris and Ui (2005, J. of Econ. Theory) for games with a saddle function. Our result generalizes sufficient conditions for zero-sum and best-response potential games.

Matias Nunez

CNRS-Cergy

Hybrid Procedures

(Joint work with Yukio Koriyama )

We consider hybrid procedures: a first step of reducing the game by iterated elimination of weakly dominated strategies (IEWDS) and then applying an equilibrium refinement. We show that the set of perfect/proper outcomes of a reduced normal-form game might be larger than the set of the perfect/proper outcomes of the whole game by applying IEWDS. In dominance solvable games in which all the orders of IEWDS select a unique singleton in the game, the surviving outcome need not be a proper equilibrium of the whole game. However, in generic dominance solvable games that satisfy the transference of decision maker indifference condition, the surviving outcome coincides with the unique stable one and hence is proper. We finally apply hybrid procedures in voting games and use them to evaluate coordination failures of strategic voters under plurality voting.

Marius-Ionut Ochea

University of Amsterdam

Evolution of Reciprocity in Asymmetric Social Dilemmas

(Joint work with Aart de Zeeuw, Tilburg University, NL)

We study the evolutionary success of a generalized trigger strategy within an asymmetric, n-person Prisoner's Dilemma environment with application to the evolution of cooperation in environmental commons. Preliminary results suggest that there exists regions in the relevant parameter space - i.e. discount factor, the two types' low/high thresholds, the asymmetric benefits/costs, etc - such that (partial) cooperation may emerge as long-run attractor of any monotone selection evolutionary dynamic in such asymmetric dilemmas.

Ram Orzach

Oakland University

Common-Value All-Pay Auctions with Asymmetric Information

(Joint work with Ezra Einy, Ori Haimanko, Aner Sela)

We study two-player common-value all-pay auctions (contests) with asymmetric information under the assumption that one of the players has an information advantage over his opponent. We characterize the unique equilibrium in these contests, and examine the role of information in determining the players' expected efforts, probabilities of winning, and expected payoffs. In particular, we show that the players always have the same probability of winning the contest, and that their expected efforts are the same, but their expected payoffs are different. It is shown that budget constraints may have an unanticipated effect on the players' expected payoffs, i.e., a player's information advantage may turn into a payoff disadvantage.

Sergio Parreiras

The University of North Carolina at Chapel Hill

A Tortoise And A Hare Race, Part I: Finite Horizon

(Joint work with Justin Joffrion)

We study a dynamic, all-pay auction under complete information. At each round, two contestants (who may have distinct valuations for the prize) simultaneously pick effort levels. The winner is the player with the highest accumulated effort at the last round. The cost of effort is separable across rounds and convex within each round. For two or more rounds, multiple subgame perfect equilibria with varying degrees of rent dissipation may exist. Decreasing the elasticity of inter-temporal effort substitution breaks down the equilibria with low rent dissipation, whereas increasing valuation asymmetries breaks down the equilibria with high rent dissipation.

Gregory Pavlov

University of Western Ontario

Correlated equilibria in zero-sum games with incomplete information

We study the relation between Nash equilibrium and different notions of correlated equilibrium in the two-player zero-sum games with incomplete information. It is known that in the zero-sum games with complete information the set of payoffs that can be achieved by correlated equilibrium coincides with the Nash equilibrium payoffs. We show that in the zero-sum games with incomplete information a similar payoff equivalence holds between Nash equilibrium and the following solution concepts: strategy correlated equilibrium, agent normal form correlated equilibrium, and belief invariant Bayesian solution. The payoff equivalence also holds between Nash equilibrium and communication equilibrium, and the equivalence continues to hold even in the environments where the players can communicate their private information in a partially verifiable way, as long as the players have an option to remain silent. However, we show that the payoffs under Nash equilibrium are not always the same under non-belief invariant Bayesian solution and Bayes correlated equilibrium. We characterize the payoffs under the last two solution concepts and relate our results to the literature on comparison of information structures in the zero-sum games.

Ahmad Peivandi Karizbodaghi

Northwestern University

Random allocation of bundles

(Joint work with NA)

For the case in which agents have arbitrary preferences over bundles of indivisible objects and monetary transfers are impermissible, I propose a randomized mechanism that generalizes the well-known probabilistic serial mechanism. This generalized mechanism returns an ordinally efficient assignment. It is asymptotically strategy-proof, asymptotically envy-free, and satisfies equal treatment
of equals. I also propose a cardinal mechanism, which returns a randomized assignment that approximates a competitive equilibrium with equal income. It satisfies ex-ante envy-freeness and efficiency, and asymptotically envy-freeness. Moreover, this mechanism is strategy proof in the continuum.

Steven Perkins

University of Bristol

Stochastic Fictitious Play with Continuous Action Sets

(Joint work with David S. Leslie)

Continuous action space games form a natural extension to normal form games with finite action sets. However, whilst learning dynamics in normal form games are now well studied, it is not until recently that their continuous action space counterparts have been examined. We extend stochastic fictitious play to the continuous action space framework. In normal form games the limiting behaviour of a discrete time learning process is often studied using its continuous time counterpart via stochastic approximation. In this paper we study stochastic fictitious play in games with continuous action spaces using the same method. This requires the asymptotic pseudo-trajectory approach to stochastic approximation to be extended to Banach spaces. In particular the limiting behaviour of stochastic fictitious play is studied using the associated smooth best response dynamics on the space of finite signed measures. Using this approach, stochastic fictitious play is shown to converge to an equilibrium point in single population negative definite games, two-player zero-sum games and N-player identical interest games, when they have Lipschitz continuous rewards.

William Phan

University of Rochester

Economies with Replicable Objects

Agents can replicate and transfer indivisible objects. Replication and transfer take a unit of time, and agents collectively have a limited amount of time. How should agents transfer objects? We study efficiency, strategy-proofness, withholding-proofness, and introduce a new axiom based on the concept of reciprocity. We show that no mechanism satisfies all four properties.

Greg Plaxton

University of Texas at Austin

A Simple Family of Top Trading Cycles Mechanisms for Housing Markets with Indifferences

(Joint work with C. Gregory Plaxton)

Recently, two new families of strategyproof mechanisms have been presented for housing markets with indifferences. These mechanisms produce a Pareto-efficient core allocation, and produce a strict core allocation when the strict core is nonempty. We propose a novel family of mechanisms and prove that this family achieves the same combination of properties. Our family of mechanisms is based on a generalization of the top trading cycles algorithm. We establish a confluence property of our algorithm, and use this property to establish that the associated mechanisms are strategyproof. We also provide a simple $O(n^3)$-time deterministic implementation of our family of mechanisms, where $n$ denotes the number of agents.

Martin Pollrich

Humboldt University Berlin

On the benefits of mediation in contracting problems with limited commitment

This paper demonstrates that the restriction to one-shot communication mechanisms in environments where the mechanism designer cannot fully commit to the outcome induced by the mechanism is overly restrictive. I show that an indirect communication mechanism yields strictly larger payoffs, compared to the best one-shot communication mechanism. One-shot direct mechanisms imply randomization by some agents type, which can be better controlled using a mediated mechanism. The latter allows for breaking indifference conditions and increases the flexibility of the mechanism designer. These results suggest a re-examination of existing literature on related problems, where the restriction to one-shot face-to-face communication is made without justification by a revelation principle.

Cheng-Zhong Qin

UC Santa Barbara

A Unification of Solutions to the Bargaining Problem

(Joint work with Claus-Jochen Haake)

We establish axioms for solutions to the bargaining problem that characterize a unique solution up to specifications of the distribution and substitution parameters of the CES function. Well-known axiomatic solutions correspond to our solution with specific values for the distribution and substitution parameters. Our results provide a unification of solutions to the bargaining problem, which is useful for comparing and characterizing various axiomatic solutions among other applications.

Andreas Reischmann

AWI, Heidelberg University

A conditional contribution mechanism for the provision of public goods

In experiments on public good problems about half the subjects have been found to be conditional cooperators. I use this knowledge to construct mechanisms in public good settings without transfers and with voluntary participation. In those mechanisms all agents have the options of freeriding, conditional and unconditional cooperation. For the equilibrium analysis of the mechanisms a new concept is introduced, which I call Unexploitable Better Response Dynamics. The equilibrium outcomes of the mechanisms under those dynamics turn out to be those Pareto optimal allocations that are strict Pareto improvements over the status quo with no contributions.

Philip J. Reny

University of Chicago

Sequential Equilibria of Multi-Stage Games with Infinite Sets of Types and Actions

(Joint work with Roger Myerson)

Guided by several key examples, we formulate a definition of sequential equilibrium for multi-stage games with infinite type sets and infinite action sets, and we provide conditions under which it exists.

Javier Rivas

University of Leicester

Deliberation, Leadership and Information Aggregation

(Joint work with Carmelo Rodriguez-Alvarez, Universidad Complutense de Madrid)

We analyze committees of voters who take a decision between two options as a two-stage process. In a discussion stage, voters share non verifiable information about a private signal concerning what is the best option. In a voting stage, votes are cast and one of the options is implemented. We introduce the possibility of leadership whereby a certain voter, the leader, is more influential than the rest at the discussion stage even though she is not better informed. We study information transmission and find, amongst others, a non-monotonic relation between how influential the leader is and how truthful voters are at discussion stage.

Frank Rosar

University of Bonn

Optimal procurement and outsourcing of production in small industries

I study the interaction between optimal procurement and outsourcing of production in small industries. First, two sellers decide about outsourcing. By outsourcing, a seller loses information about the costs of producing to his supplier. Then the buyer designs the procurement mechanism and sellers who outsourced production subcontract with their respective suppliers. The focal equilibrium might exhibit bilateral outsourcing although outsourcing is modeled to have no direct positive effects. When a seller is able to extract his supplier’s rent ex ante, the focal equilibrium exhibits bilateral outsourcing for any distribution of production costs satisfying a regularity condition.

Al Roth

Stanford University

Kidney Exchange: Where We've Been and Where We May Be Headed

To be posted...

Asha Sadanand

University of Guelph

Signalling Games with Multiple Senders

In this paper I explore information signalling when the same information is held by more than one informed party. Generally, having more informed parties increases the times when signals can be used to convey the information to uninformed parties and implement separating equilibria. Also of importance is the context of the game between the informed players, and whether the prefer to coordinate or not in signalling the information. I show that the traditional approach to forward induction does not give appropriate results. Instead I suggest that the approach taken in Manipulated Nash Equilibrium gives results that are intuitively superior.

Bruno Salcedo

PennState

Implementation without commitment in moral hazard environments

I define a solution concept for strategic form games called interdependent-choice equilibrium. It is an extension of correlated equilibrium, in which the mediator is able to choose the timing of his signals and observe the actions taken by the players. The set of interdependentchoice equilibria is nonempty and is given by a finite set of affine inequalities. It characterizes all the outcomes that can be implemented in single shot interactions without the use of binding contracts or any other form of delegation. The results can also be interpreted as robust predictions for environments in which the rules of the game (e.g. order of play and information structure) are unknown.

Maryam Sami

Stony Brook University

Financial Contagion and Reputational Concerns of Fund Managers in Diversified Funds

We discuss an infinite horizon delegated portfolio management problem with two risky assets and one risk free bond. We have four types of managers from absolutely uninformed about the risky asset values to perfectly informed of the asset values and three types of funds; only specialized on one risky asset and the risk free bond, or diversified on both risky assets and riskless bond. The types of managers are private information while the types of funds is common knowledge. Funds hire the managers and delegate the investment decision to them. In the beginning of each day, unemployed managers seek an employment by strategically signalling for which funds they want to work. Given the signals, funds randomly pick a manager from the ones willing to be matched with them and offer a contract that pays a fixed share of the return at the end of each period and retains the manger for the next period only if his investment decision has been successful. We first show that the compensation scheme and the firing threat is partially separating informed, partially informed and absolutely uninformed managers. In particular, the managers only informed of asset 1(2) only accept the offers of the funds specializing in markets 1(2) and absolutely informed managers only accept the offer of diversified funds while absolutely uninformed managers are accepting any offer from any fund. Hence, there exists a nonzero measure of absolutely uninformed managers in any fund.
Second, we show that uninformed managers hired by diversified funds faced with the firing threat transmit shocks from one market to the other, resulting in price contagion.

Larry Samuelson

Yale University

Investment and Matching

This paper examines a market in which buyers and sellers must first make investments, and then match to produce and split a surplus whose size is determined by their investments.We are especially interested in identifying conditions under which the post-investment matching process created incentives for the agents to take efficient investments.We identify fairly general conditions under which there exists an equilibrium in which investments are efficient, as well as equilibria featuring inefficient investments.We identify somewhat more restrictive conditions under which equilibria are “constrained efficient,” allowing us to characterize inefficient investments as reflecting either coordination failures or missing markets.We also provide a more general proof of the existence of equilibrium that clarifies the underlying economic forces, and we draw connections to implementation in principal-agent problems.

Farishta Satari

CUNY Graduate Center

Cheap Talk in the Presence of an Audience

We extend the ideas of Grice on cooperative communication and the ideas of Crawford, Farrell, Rabin, Sobel, and Stalnakar on communication with partially overlapping interests. In our work, we introduce a third player in the communication game, called audience, and analyze the ramifications of his presence. We show that the way the speaker talks depends not only on players’ knowledge states (expressed using Kripke Structures), but also on her relationship with the audience and how ethical she perceives the audience to be.

Marco Scarsini

SUTD

Dynamic Congestion Games: The Price of Seasonality

(Joint work with Tristan Tomala)

This paper studies dynamic congestion games over simple networks with seasonal arrival flows. We compute long-run average equilibrium and optimal costs and characterize the associated flows. We prove that optimal flows are unique and that equilibrium flows coincide with optimal flows after a finite number of stages. We study in details the case of uniform arrivals. Then, we introduce a measure of discrepancy between a periodic distribution of arrivals and the uniform one. The optimal and equilibrium costs induced by a periodic sequence of arrivals are deduced from those induced by uniform arrivals by adding this same quantity. Computations and bounds on the price of anarchy are derived.

Gijs Schoenmakers

Maastricht University

Algorithms for finding subgame perfect equilibria in recursive games with perfect information

(Joint work with J. Flesch, J. Kuipers, A. Mashiah-Yaakovi, E. Solan, K. Vrieze)

In our paper ”Pure subgame-perfect equilibria in free transition games” ([4]) we first presented an iterative method to find (and thereby prove the existence of) subgame-perfect equilibria in a subclass of perfect information games called free transition games. After that, in ([1]) we transformed the method into an algorithm that could be used to find subgame-perfect epsilon-equilibria for positive recursive games with perfect information. In more recent papers we updated the algorithm, so that it could be used for more general classes of games (cf. ([3]) and ([2])). In this presentation we discuss
how each version of the algorithm works. Some of the main concepts are alpha-values, (game-)plans, viability and vulnerability. A part of the discussion in on the issues that makes it a challenging task to get the algorithm to work in each new class, including the class that we are currently working on.

References:

[1] Flesch J., Kuipers J., Schoenmakers G. and Vrieze K. (2010): Subgame perfection in positive recursive games with perfect information. Mathematics of Operations Research 35, 193–207.
[2] Flesch J., Kuipers J., Schoenmakers G. and Vrieze K. (2013): Subgame-perfection in free transition games. European Journal of Operational Research 228, 201–207.
[3] Flesch J., Kuipers J., Mashiah-Yaakovi A., Schoenmakers G., Solan E. and Vrieze K. (2010): Perfect-information games with lower-semi-continuous payoffs. Mathematics of Operations Research 35, 742–755.
[4] Kuipers J., Flesch J., Schoenmakers G. and Vrieze K. (2008): Pure subgame-perfect equilibria in free transition games. European Journal of Operational Research 199, 442–447.

Marc Schröder

Maastricht University

A non-cooperative analysis of the estate division problem

(Joint work with Hans Peters, Dries Vermeulen)

This paper considers the estate division problem from a non-cooperative perspective. The integer claim game initiated by O'Neill (1982) and extended by Atlamaz et al. (2011) is generalized by allowing for an arbitrary sharing rule to divide every interval among the claimants. Our main focus is on games that use the constrained equal awards rule, the constrained equal losses rule, or the Talmud rule as sharing rule. A full characterization of the set of Nash equilibria with corresponding payoffs is obtained for these games. It is shown that for a subset of problems, the Talmud rule is the only rule from a particular family of rules that always results in an equilibrium payoff. A variation on the claim game is considered by allowing for arbitrary instead of integer claims.

Tadashi Sekiguchi

Kyoto University

Multimarket Contact under Demand Fluctuations: A Limit Result

The present paper studies repeated oligopoly where the firms compete with price in multiple markets. The markets are subject to independent, stochastic fluctuations in demands. The literature points out that while the demand fluctuations generally hinder collusion, the multimarket contact sometimes facilitates it. We show that on an intermediate range of discount factors where only partial collusion is possible under a single market, the difference between the profit under full collusion and the maximum equilibrium profit converges to zero, if the number of markets goes to infinity. Thus the collusion-deterrence effects of fluctuated demands completely vanish in the limit.

Eran Shmaya

Northwestern University

Compressed equilibrium in large repeated games with incomplete information

(Joint work with Ehud Kalai)

In equilibrium of large (many players) Bayesian games, stability properties fail when player types are interdependent. But when the game is played repeatedly, the players “learn to be independent” and stability is restored. To have a more robust and manageable analysis of such games, we develop a new equilibrium concept called compressed equilibrium. Defined for semi-anonymous games, compressed equilibrium is significantly easier to compute, is independent of the number of players and repetitions of the game, and it becomes an epsilon Nash equilibrium as the number of players increases.

Eilon Solan

Tel Aviv University

Stopping games

Stopping games are dynamic games in which the players possess symmetric information and their only decision is when to stop. These models include, among others, preemption games and wars of attrition. I will survey the results of the last decade in this area, both in discrete and continuous.

Robert Somogyi

Ecole Polytechnique

Bertrand-Edgeworth competition with substantial product differentiation

Since Kreps and Scheinkman's seminal article a large number of papers have analyzed capacity constraints' potential to relax price competition. However, the ensuing literature has assumed that products are either perfect or very close substitutes. Therefore none of them has investigated the interaction between capacity constraints and substantial local monopoly power. The aim of the present paper is to shed light on this question using a standard Hotelling setup. The high level of product differentiation results in a variety of equilibrium firm behavior and it generates at least one pure strategy equilibrium for any capacity level. Thus the presence of local monopoly power challenges one of the most general findings about Bertrand-Edgeworth competition: the non-existence of pure strategy equilibria for some capacity levels.

Sylvain Sorin

Université Pierre et Marie Curie - Paris 6

On Reversibility and Oscillations in Zero-sum Discounted Stochastic Games

(Joint work with G. Vigeral)

We show that by coupling two well-behaved dynamical optimization problems one can construct two-person zero-sum stochastic games with nite state space having oscillating discounted values. This unifies and generalizes recent examples due to Vigeral (2013) and Ziliotto (2013).

Marilda Sotomayor

Universidade de São Paulo

Modeling Cooperative Decision Situations: The Deviation Function Form and The Equilibrium Concept

Rosenthal (1972) points out that the coalitional function form may be insufficient to analyze some strategic interactions of the cooperative normal form. His solution consists in representing games in effectiveness form, which explicitly describe the set of possible outcomes that each coalition can enforce by a unilateral deviation from any proposed outcome.

This paper detects some non-appropriateness of the effectiveness representation with respect to the stability of outcomes against coalitional deviations. In order to correct such inadequacies, it is then proposed a new model, called deviation function form, which modifies Rosenthal’s setting by also modeling the coalition structure and by incorporating new coalitional interactions, which support the agreements proposed by deviating coalitions. The concept of stability of the matching models, viewed as a cooperative equilibrium concept, is then translated to any game in the deviation function form and is confronted with the traditional notion of core. Precise answers are given to the questions raised.

Todd Stambaugh

CUNY Graduate Center

Coincidence of Two Solutions to Nash's Bargaining Problem

(Joint work with Todd Stambaugh)

John Nash (1950) gave an elegant solution to the bargaining problem using his somewhat controversial IIA axiom. Ehud Kalai and Meir Smorodinsky (1975) gave a diff erent solution replacing the IIA condition by their own Monotonicity condition. While the two solutions do not coincide in general they obviously do so when the problem is symmetric. Are there other cases where the two solutions coincide? Indeed there are and we give a complete characterization.

Nora Szech

University of Bonn

Morals and Markets

(Joint work with Armin Falk)

The possibility that market interactions may erode moral values is a longstanding, but controversial, hypothesis in the social sciences, ethics and philosophy. To date empirical evidence on decay of moral values through market interaction has been scarce. This paper presents controlled experimental evidence on how market interaction changes the valuation of harm and damage done to third parties, i.e., to those who suffer from trade but who are not trading themselves. The context we study is the trade-off between life and money. Subjects decide between the life of a mouse and receiving a monetary amount. We compare individual decisions about killing the mouse to decisions made in a bilateral and a multilateral market. In both market situations, the willingness to kill is substantially higher than in individual decisions. Furthermore, in the multilateral market, prices for life deteriorate tremendously. In contrast, for consumption choices that do not have a moral dimension, differences between individual and market institutions are small.

Marek Jerzy Szopa

University of Silesia

Nash Equilibria of the Quantum Prisoner's Dilemma

(Joint work with Marek Szopa)

The Prisoner’s Dilemma [PD] is the best known example of a two-person simultaneous game for which the Nash equilibrium is far from Pareto optimal result. In this paper we define a quantum PD, for which players' strategies are defined as rotations of the SU(2) group, parameterized by three angles. Quantum strategies are correlated through the mechanism of quantum entanglement and the result of the game is obtained by the collapse of the wave function. Classical PD is a particular case of the quantum game for which the set of rotations is limited to one dimension. Each quantum strategy can be, by particular choice of counter-strategy, interpreted as 'cooperation' or 'defection'. Quantum PD has more favourable Nash equilibria than the classical PD, and they are close to the Pareto optimal solutions. With proper selection of strategies PD can be played as a classic zero sum game. In this paper are shown some examples of economical phenomena such as the price collusion and the chess strategy, which reflect the Nash equilibria of quantum PD.

Noam Tanner

Yale University

Optimal Delegation Under Uncertain Bias

(Joint work with N/A)

We study a principal-agent relationship without monetary transfers. The principal is uncertain of the agent's preferences. We show that if the principal is restricted to offering convex menus (menus consisting of only convex sets), then a pooling menu, a menu consisting of a single delegation set, is optimal. We also show that the restriction to convex menus is without loss in various settings. Thus, in these settings, the optimal menu consists of a single interval. We also show that the optimal pooling menu is convex (in all settings studied). In addition, we provide some comparative statics. Finally, this paper generalizes a main result of Melumad and Shibano (1991) to a larger class of loss functions. The proof of this generalization provides additional intuition for the result: non-convex menus are mean-preserving spreads of convex menus. Thus, nonconvex menus are suboptimal for the principal.

Ryan Tierney

University of Rochester

Strategy-proofness and Asymptotic Efficiency in Exchange Economies

(Joint work with n/a)

It is well known that Pareto efficiency, strategy-proofness, and equal-division lower bound are incompatible in classical economies. We ask if there are any strategy-proof rules satisfying the equal-division lower bound that are asymptotically efficient, as population size increases. We find that even on the domain of quasilinear preferences there are not. Moreover, the result does not depend on “strange” or “knife-edge” economies. With one-dimensional type-spaces, however, there is hope. We find a class of rules that are both easy to compute and asymptotically efficient for such a reduced domain. We note that the computational simplicity of these rules compares favorably with VCG mechanisms in large economies and that they are budget balanced. Furthermore, we conjecture that their asymptotic efficiency extends somewhat beyond one-dimensional type-spaces.

Tristan Tomala

HEC Paris

Approximate Implementation In Markovian Environments

(Joint work with Ludovic Renou)

We consider dynamic implementation problems with evolving private information (according to Markov processes). A social choice function is approximatively implementable if there exists a dynamic mechanism such that the social choice function is implemented an arbitrary large number of times with arbitrary high probability in every (communication) equilibrium.

We show that if a social choice function is strictly efficient in the set of social choice functions that satisfy an undetectability condition, then it is approximatively implementable. We revisit the classical monopolistic screening problem and show that the monopolist can extract the full surplus in almost all periods with arbitrary high probability.

Peter Troyan

Stanford University

Implementing Diversity in School Choice

(Joint work with Peter Troyan and Daniel Fragiadakis)

Diversity considerations are important in many matching markets, with the most prominent example being school choice. A simple way to achieve diverse student populations is to impose minimum and maximum quotas on the number of students of each type at each school. This causes significant problems for popular matching mechanisms (which have no input for such minimum quotas), leading many markets to impose stricter artificial caps in order to guarantee all lower quotas are satisfied. In this paper, we provide strategyproof mechanisms which guarantee the desired diversity at each school, while recovering inefficiencies that arise with artificial caps. In addition, we show that our mechanisms satisfy good fairness and nonwastefulness properties, while still providing optimal incentives.

Paolo Turrini

Imperial College London

Non-cooperative games with preplay negotiations

(Joint work with Valentin Goranko and Paolo Turrini)

We consider an extension of strategic normal form games with a phase of negotiations before the actual play of the game, where players can make binding offers for transfer of utilities to other players after the play of the game, in order to provide additional incentives for each other to play designated strategies. Such offers are conditional on the recipients playing the specified strategies and they effect transformations of the payoff matrix of the game by accordingly transferring payoffs between players. We introduce and analyze solution concepts for 2-player normal form games with such preplay offers under various assumptions for the preplay negotiation phase and obtain results for existence of efficient negotiation strategies of the players. Then we extend the framework to coalitional preplay offers in N-player games, as well as to extensive form games with inter-play offers for side payments.

Amparo Urbano

University of Valencia

Local Coordination and Global Congestion in Random Networks

(Joint work with Ivan Arribas)

This paper analyzes the impact of local and global interactions on individuals’ action choices. Players are located in a network and interact with each other with perfect knowledge of their neighborhood and probabilistic knowledge of the complete network topology. Each player chooses an action, from some finite set, which imposes an externality on their neighbors as well as an externality on the complete network. Players deal with two opposing forces: they obtain utility from sharing their choices with their neighbors (positive local externality) but suffer disutility from sharing the same choice with all members of the network (negative global externality). Economic and social phenomena exhibiting these features are: the adoption of cost-reducing innovation, clusters of firms, time schedule choices, the adoption of subcultures and fads, among others. We find the conditions for the existence of all Bayesian Nash equilibria and translate them to a characterization in terms of the main properties of the network topology. The balance between local satisfaction and global dissatisfaction partially explains the equilibrium outcome. The players who finally decide the type of equilibria are those that are either highly connected (hubs) or poorly connected (peripherals) to the others. On the one hand, hubs try to coordinate their action choices, which will depend on the perceived congestion. On the other, peripherals are only worried about congestion and play the less selected actions of the network. Some examples illustrate our main results as well as the failure of equilibrium existence for some congestion costs.

Nicolas Vieille

HEC Paris

Stochastic games: a quick overview

Upon the request of the organizers, I will present a quick overview of selected results in stochastic games, starting from the celebrated paper of L. Shapley, emphasizing the contributions of J.-F. Mertens, and including very recent developments and open problems.

Bernhard Von Stengel

London School of Economics

Game Theory Explorer - Software for the Applied Game Theorist

We describe and demonstrate a software tool for creating and analyzing noncooperative games. The Game Theory Explorer (GTE) has a graphical user interface which is opened in a web browser. It allows to create extensive games or games in strategic form. The games can be exported to graphical file formats. The Nash equilibria of the game are computed and displayed, currently implemented for 2-player games. The software is directed at people who are familiar with game theory, such as researchers and students in economics, but they do not have to be experts in algorithms for solving games.

The development of GTE has been supported by "Google Summer of Code" studentships for open-source software. It is part of the Gambit project, which was initiated over 20 years ago by Richard McKelvey and is now maintained by Theodore Turocy.

Yun Wang

University of Pittsburgh

An Experimental Investigation on Belief and Higher-Order Belief in the Centipede Games

This paper explores people's beliefs behind non-backward induction behavior in laboratory centipede games. We elicit players' beliefs about opponents' strategies and 1st-order beliefs. The measured beliefs help us to infer the conditional probability systems of both players. The inferred CPS's and players' actual strategy choices identify why they fail to reach the BI outcomes. First, we examine whether the player's strategies are best response to the measured beliefs, i.e. players are rational. In all the treatments, the frequency of players' being rational is significantly less than probability 1; but the frequency in the Constant-Sum treatment is significantly higher than that in other treatments. Second, as regarding players' beliefs and higher-order beliefs of rationality, we find that neither common initial belief of rationality nor common strong belief of rationality always holds. Nevertheless, in the Constant-Sum treatment both the frequency of players' initially believing in others' rationality and the frequency of players' higher-order initial belief of rationality are significantly than those in the other treatments.

Ben Wang

National University of Singapore

An Epistemic Characterization of RSCE

(Joint work with Xiao Luo; Ben Wang)

Dekel et al. (J Econ Theory 89 (1999) 165-185) offered a solution concept of “rationalizable self-confirming equilibrium (RSCE)” as the steady state where rational individuals observe the played actions and use the information about opponents’ payoffs in forming the beliefs about opponents’ behavior off the equilibrium path. In this paper we investigate epistemic conditions for RSCE from a decision-theoretic point of view. Within a standard semantic framework, we formulate and show, by using the notion of “conditional probability system (CPS),” that RSCE is the logical consequence of common knowledge of rationality and mutual knowledge of the actions along the path of play. In this paper, we also apply this epistemic approach to other related solution concepts such that self-confirming equilibrium (SCE) and sequential rationalizable self-confirming equilibrium (SRSCE).

Guocheng Wang

Chinese Academy of Social Sciences

Game Modeling and Strategic Behavior Analysis of Stakeholders in Public Goods Provision

(Joint work with Guocheng Wang; Ye Tian)

The utility of public goods vary with the behaviors of stakeholders (players), and it is appropriate to study effective supply and management of Public Goods with game modeling and analysis. In the first section of this paper, the definition of integrated water resources management(IWRM), the importance of stakeholder participation in water management and some models as well as methods that have been applied for this issue are illustrated. Following this, the framework of analysis is elaborated. Within this section, the scenario and aims are shown, and it is claimed that game theory is the main approach, which includes both cooperative games and non-cooperative games. To achieve the aims of the public project, five approaches from game theory are able to cover the entire process of the project, and the fourth approach on interest compensation mechanism is the highlight of the research. After this, the interest compensation mechanism is demonstrated in the model section, and is proved to be an incentive compatible mechanism that makes each stakeholder choose to behave in accordance with the interest of the entire project. The Clarke-Groves mechanism is applied in establishing the model, and the utility change by the comparison among stakeholders (defined as the comparison effect) is involved. In the application section, a water project is analyzed in consideration of various stakeholders, and other possible applications are also indicated.

Daniel Wood

Clemson University

Cognitive Biases in Stochastic Coordination Games and Their Evolution

I model the evolution of behavior in small groups whose members play pairwise 2x2 pure coordination games. Players follow a best-response dynamic with errors which are generated by a fixed cognitive bias, such as the representativeness heuristic. Mistakes in strategy choice impair successful coordination, but they also cause the group to occasionally switch between equilibria. If which equilibrium generates higher payoffs switches at a slower rate than the strategy-updating process, then errors create a positive externality for other players because the group returns to high-payoff equilibria faster. I characterize group members' payoffs generated by this dynamic for several error-generating biases, including limited cognition, the representativeness heuristic, the false-consensus effect,and loss aversion. Behavioral biases produce larger externalities relative to simply higher error rates. I then analyze how these biases would evolve in a setting with group structure. Group selection partially internalizes the positive externalities, stabilizing a population state in which some players have biases and others do not.

Rupei Xu

University of Minnesota--Twin Cities

Altruism in Local and Global Network Topologies: A Game Theoretic Study of Resource Allocation in Social Networks

The assumption that players are all rational and self-interested has dominated the Game Theory and Economics for centuries. However, there is a lot of altruistic phenomenon in daily life. How to understand the altruism? This paper gives a bridge of selfish and altruistic types of players and uses the resource allocation game in social networks to explain the relationship between altruism and local and global network structures.

Zibo Xu

Stockholm School of Economics

Convergence of best response dynamics in extensive-form games

We prove that, in all finite generic extensive-form games of perfect information, a continuous-time best response dynamic always converges to a Nash equilibrium component. We show the robustness of convergence by an approximate best response dynamic: whatever the initial state and an allowed approximate best response dynamic, the state is close to the set of Nash equilibria most of the time. In a perfect-information game where each player can only move at one node, we prove that all interior approximate best response dynamics converge to the backward induction equilibrium, which is hence the socially stable strategy in the game.

Ling Yang

University of Pittsburgh

Partisan Voting and Uncertainty

In this paper, we study a model in which partisan voting is rationalized by Knightian decision theory under uncertainty (Bewley, 1986). When uncertainty is large, some voters become hard-core supporters of their current party due to status quo bias. We characterize equilibria in a setting similar to Krishna and Morgan (2012). Under Knightian uncertainty, mixed-strategy equilibrium is more flexible, because indifference among strategies used in equilibrium is no longer required. With costly information, there always exists an equilibrium. In some scenarios, swing voters acquire positive amount of information in equilibrium.

Seung Han Yoo

Korea University

Learning a Population Distribution

(Joint work with Seung Han Yoo)

This paper introduces a dynamic Bayesian game with an unknown population distribution. Players do not know the true population distribution and assess it based on their private observations using Bayes' rule. First, we show the existence and characterization of an equilibrium in which each player's strategy is a function not only of the player's type but also of experience. Second, we show that each player's initial belief about the population distribution converges almost surely to a "correct" belief.

Jung You

Rice University

Optimal VCG Mechanisms to Assign Multiple Bads

For the problem of assigning identical economic “bads” (for example, costly tasks or undesirable objects), VCG mechanisms achieve efficient allocations via money transfers. However, they produce arbitrarily large budget surpluses or deficits. We construct a two-dimensional performance index of a VCG mechanism to minimize its budget surplus and deficit in the worst case. Using our index, we can develop asymptotically budget-balanced mechanisms not only for the case of bads but also for the case of “goods.” We find individual rationality creates a great asymmetry between budget surplus and deficit particularly in the case of bads. As more agents participate, a very minute amount of deficit can replace unit surplus to achieve budget balance. For the case of economic goods, regardless of individual rationality, unit surplus can only be replaced with unit deficit. This result suggests that the problem of assigning bads deserves more
careful investigation.

Walter Yuan

MobLab Inc

Learning by Playing: Interactive games for game theory classroom

(Joint work with Rachel Bodsky, Stephanie Wang, and Thomas Palfrey)

While the benefit of learning by playing has been long-established in education, experiments have not gained similar traction in social science classrooms, largely due to lack of accessible, scalable, and robust platforms, both hardware and software, for such real time interactions. At MobLab, we are aiming at developing a comprehensive solution that combines all the necessary technical and pedagogical components to improve the accessibility of classroom experiments. The games we have implemented thus far, such as many variations on bargaining, markets, auctions, voting, matrix games, etc., are particularly relevant for topics typically covered in a game theory class.

Since the fall 2012, We have conducted feasibility studies at over 40 universities on playing interactive games using mobile technologies in classrooms. We found that students were engaged with our context-rich game interfaces and needed very little instructions on how to play the games. By making the games available on browsers, phones, and tablets, our solution completely eliminated the necessity of a computer lab. Our instructor console made play-as-you-go a reality in the classroom through its simple drag-n-drop experiment configuration, comprehensive game parameter set, real-time monitoring and instant game summaries. Finally, initial results from the classroom experiments were shown to be consistent with what has been reported from controlled laboratory experiments, demonstrating the validity of both the technology and methodology.

Shmuel Zamir

The Hebrew University of Jerusalem

Representations of constitutions under incomplete information

(Joint work with Bezalel Peleg)

We model constitutions by effectivity functions. We assume that the constitution is common knowledge among the members of the society. However, the preferences of the citizen are private information. We investigate whether there exist decision schemes (i. e., functions that map profiles of strategies to lotteries on the set of social states), with the following properties: i) The distribution of power induced by the decision scheme is identical to the effectivity function under consideration; and ii) the (incomplete information) game associated with the decision scheme has a Bayesian Nash equilibrium in pure strategies. If the effectivity function is monotonic and superadditive, then we find a class of decision schemes with the foregoing properties.

Yi Zhang

Singapore Management University

Anonymous Matching and Group Reputation

(Joint work with Huan Wang)

We explore what group reputation is and model its formation and evolution. Based solely on group signals, we define a player's group reputation as the belief that others have about the characteristics of the group the player belongs to. A model of group reputation of civil servants is constructed to characterize the strategic behavior of potential bribers and civil servants. We analyze the possible steady states and their feasible conditions under the anonymous matching and acquaintance matching respectively, as well as the dynamic analysis. Then, we show that the regime change from acquaintance matching to anonymous matching will cause the rampancy of corruption if the supervision effort level is small. Finally, we investigate the effectiveness of anti-corruption policy and show that to turn around a high level of corruption, the level of supervision effort has to reach some minimum level. In addition, the effectiveness of the anti-corruption policy is not monotonic with respect to the level of supervision effort. As there are two types of corruption behavior of civil servants: accepting bribes and dereliction of duty, anti-corruption should work along both lines.

Yi Zhang

Singapore Management University

Robust Information Cascade with Endogenous Ordering

We analyze a sequential decision model with one-sided commitment in which decision makers are allowed to choose the time of acting (exercising a risky investment option A) or waiting. We characterize information cascade under endogenous ordering and show that with endogenous ordering, if the number of decision makers is large and decision makers are patient enough, at any fixed time, nearly all decision makers wait due to the negligible information disclosed. In this case, if decision makers can be forced to move with an exogenous order, the resulting equilibrium is more efficient because exogenous ordering tends to aggregate more information.

Hanzhe Zhang

University of Chicago

Reserve Price Auctions in a Dynamic Heterogeneous Goods Market

This paper examines the steady state of a large market where the goods are differen- tiated but stochastically equivalent (e.g. houses, used books, oil drilling rights). The equilibrium selling mechanism is a standard auction with the optimal reserve price determined by not only the buyer value distribution in the static setting but also the market environment. In particular, the reserve price increases when there is more inflow of buyers and the buyers become more impatient, but the change in it is ambiguous if buyers exit the market more often or the length of a period changes. The general equilibrium welfare effects of the reserve price auctions are discussed as well.

Peio Zuazo-Garin

University of the Basque Country

Incomplete Imperfect Information and Backward Induction

We consider finite extensive-form games in which the information structure of the game --the information and choice partitions, is not common knowledge once the game is endowed with an epistemic framework similar to the ones in Aumann (1995 and 1998), and specially, Samet (2013). This approach allows for generalizing the result in Samet (2013) concerning how common belief of rationality implies backward induction to situations in which there is not common knowledge of perfect information. Instead, we consider the weaker doxastic event that there is common belief that all players believe that the rest of players have perfect information. In particular, it might be the case, not because of chance but rather as a consequence of common belief of rationality, that players behave inductively even when none of them know at which vertex they are when it is their turn to choose. Additionally, we prove that for any given tree and information structure, there exists an epistemic framework as defined by us such that the event that rationality and belief in others' perfect information are common belief is non-empty.

Felipe Zurita

Pontificia Universidad Catolica de Chile

Competitive pressure and incentives in the quality game: The reputational mechanism

(Joint work with Bernardita Vial)

We examine the incentives for the production of the high quality variety of an expe- rience good in a Walrasian market where firms may freely change their names, i.e., they may erase their past at will. Our interest is to analyze how a change in the competitive pressure from outsiders affects incentives. Besides affecting prices, competitive pressure in our model also affects the threshold of reputation below which firms choose to erase their past. We find that an increase in the competitive pressure may boost incentives through an increase in the price differential between qualities, and also –perhaps counterintuitivelly– through an increase in the “forgetfulness” of the market.