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Speakers |
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Princeton University Reputational Values for Dynamic Games (joint work with David Pearce) Abstract This talk explores how reputational perturbations serve to identify unique equilibrium outcomes in a variety of two player dynamic games with equally patient players. The unperturbed variants of these games typically have a vast multiplicity of equilibria. Among the games considered are a general class of stochastic games. The characterization for this class entails extending the definition of "Nash Bargaining with Threats" (Nash, 1953) to a stochastic game setting. This extension is of independent interest. The solution involves a natural balancing of the relative potential of players to harm their opponents and benefit themselves in terms of flow state-payoffs and (possibly endogenous) transition probabilities and the interaction of the latter with the frontier of efficient payoffs. The emphasis is on environments in which contract signing is possible. However, we conjecture that the analysis can be extended to non-contractual settings. Such an extension is already available for the purely repeated case. |
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TOBB University of Economics and Technology Thursday, July 12, 10:30, Session D Intertemporal Decision Making with Present Biased Preferences [pdf] Abstract I study the behavior of individuals who have present biased preferences when they have to complete a costly long run project. Quasi hyperbolic discounting is used in modeling preferences. I basically make the payoff structure of the project endogenous (as opposed to the literature taking it exogenous) by introducing a bargaining stage. I show that endogenizing the payoff affects agents' behavior in such a way that the exponential type completes the investment stage immediately, whereas the sophisticated type has a cyclical completion behavior. The naive type either invests immediately or postpones until the deadline. If the naive does not procrastinate, the sophisticated does worse than the naive and vice versa. Then, a bonus motive is introduced and the minimal incentive scheme to prevent inefficient procrastination is derived. I show that for naive players, the minimal incentive scheme involves an increasing reward structure and it requires higher rewards for players with higher time inconsistency. I, then, introduce partially naive hyperbolic types who potentially learn their actual preferences overtime. Without learning, they do not procrastinate as long as the perceived maximum tolerable delay is more than or equal to the current maximum tolerable delay. If the former is strictly less, then they procrastinate until the deadline. However, with learning, if the learning pace is fast enough, this is not the case. |
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Sabanci University, Istanbul University Admissions and Shortlist Matching Abstract In several countries, national centers match all of a large population of students with university departments, using individual preferences and Exam scores and Gale-Shapley stability. The role Exams play in representing the preferences of universities is likely to affect secondary education in unwanted ways. A natural remedy, keeping the Clearinghouse benefits, lies in two-stage Shortlist Matching, I propose : With initial (“preliminary”) preferences, find a stable k-matching, i.e., match every agent with a k-list of candidates. Then get agents’ rankings of their k-candidates and find a stable matching. In general and in some special cases, I give lower bounds on the number of agents who get matched within their k-lists. |
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Columbia University Toward a Rational Choice Foundation for Non-Additive Models [pdf] Abstract In the spirit of the Knightian distinction between Risk and Uncertainty, we ask the following question: when is it that a decision maker has enough information to obey the Anscombe-Aumann Subjective Expected Utility (SEU) axioms? We study information structures (i.e. partitions) on the set of the decision maker's possible priors and prove that with certain information structures the decision maker cannot obey SEU. A series of examples, one of which is a version of Ellsberg's experiments, demonstrates the relevance of such information structures. Our results pave the way towards a Rational Choice foundation for(some) non-additive models. In the final part of the talk, we discuss some preference functionals that may be thought of as a rational response to situations of Knightian Uncertainty. We argue that these functionals must take the form of Choquet integrals over a set of priors. |
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Brown University Wednesday, July 11, 03:30, Session E Robust Virtual Implementation: Toward Reinterpretation of Wilson's Doctrine [pdf] (joint work with Takashi Kunimoto, Roberto Serrano) Abstract
We consider robust virtual implementation, where robustness is the requirement that implementation succeed in all type spaces consistent with a given payoff type space as well as with a given space of first-order beliefs about the other agents’ payoff types. This last bit, which constitutes our reinterpretation of the Wilson doctrine, allows us to obtain very permissive results. Our first result is that generically, if there are at least three alternatives, any incentive compatible social choice function is robustly virtually implementable in iteratively undominated strategies. Further, we characterize robust virtual implementation in iteratively undominated strategies by means of incentive compatibility and measurability. Our characterization is independent of the presence of monetary transfers or assumptions alike, made in previous studies. Our work also clarifies the measurability condition in connection to the generic diversity of preferences used in our first result. |
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Harvard An Efficient Dynamic Mechanism [pdf] (joint work with Ilya Segal) Abstract This paper constructs an efficient, budget-balanced, Bayesian incentive-compatible mechanism for a general dynamic environment with private information. As an intermediate result, we construct an efficient, ex post incentive-compatible mechanism, which is not budget balanced. We also provide conditions under which participation constraints can be satisfied in each period, so that the mechanism can be made self-enforcing if the horizon is infinite and players are sufficiently patient. In our dynamic environment, agents observe a sequence of private signals over a number of periods (either finite or countable). In each period, the agents report their private signals, and make public (contractible) and private decisions based on the reports. The probability distribution over future signals may depend on both past signals and past decisions. The construction of an efficient mechanism hinges on the assumption of "private values" (each agent's payoff is determined by his own observations). Balancing the budget relies on the assumption of "independent types" (the distribution of each agent's private signals does not depend on the other agents' private information, except through public decisions). |
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Hebrew University of Jerusalem My Gale Abstract
I will briefly present three or four of the most beautiful, elegant and important contributions of David Gale to Game Theory. |
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PSU Friday, July 13, 03:00, Session D Ambiguous Act Equilibria [pdf] Abstract A novel approach for the study of games with strategic uncertainty is proposed. Games are defined such that players' strategy spaces do not only contain pure and mixed strategies but also contain "ambiguous act strategies", in the sense that players can base their choices on subjective randomization devices. Expected utility representation of preferences over strategy profiles consisting of such "ambiguous act strategies" is not assumed. The notions of "independent strategies" as well as "common priors" are relaxed in such a manner that they can be applied to the context of games with strategic uncertainty even though the player's preferences cannot necessarily be represented by expected utility functions. The concept of "Ambiguous Act Equilibrium" is defined. I show that the ambiguous act equilibria of a two player games in which preferences of all players satisfy Schmeidler's uncertainty aversion as well as transitivity and monotonicity are observationally equivalent to the mixed strategy equilibria of that game in the sense that a researcher who can only observe equilibrium outcomes is not able to determine whether the players are uncertainty averse or uncertainty neutral. |
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Laboratoire d'Econométrie de l'Ecole Polytechnique, A Theory of Measuring, Electing and Ranking (joint work with Rida Laraki) Abstract
The theory of social choice concerns methods for amalgamating the appreciations or evaluations of many individuals into one collective appreciation or evaluation. It has two principal applications. (1) Voting: electors in a democracy choose one among several candidates, or committee members decide on one among several courses of action. (2) Jury decisions: judges evaluate competitors - figure skaters, gymnasts, pianists, wines, ... - and rank them or classify them by level of excellence. The fundamental problem is to find a social decision function (SDF) whose inputs are messages of judges or voters and whose outputs are the jury or electoral decisions, usually rank-orderings of competitors and winners. In the real world, a judge's message is simply a message, nothing more: it is neither a preference nor an appreciation. Whatever its formal definition, a judge's or a voter's message depends on a host of factors that include the output or decision, the messages of the other judges and the social decision function that is used. The traditional model of the theory of social choice - whose origins may be traced to at least Lull (1297) and Cusanus (1433) - does not adequately treat the messages or the purposes of the judges and voters. Moreover, Arrow's (1951) and all the other impossibility and incompatibility results show that the basic problem has no acceptable solution in the context of that model. We add to this long list a negative theorem of a new kind. There is a fundamental incompatibility between winners and rank-orderings as outputs: the winner should perhaps be the third-ranked candidate of the ordering, not the first! A new model is necessary. Practice suggests a different formulation of the inputs. Olympic competitions in figure skating and gymnastics, wine competitions, competitions among pianists, flautists or orchestras, ... , all use measures or grades. Indeed, Arrow himself states "there are essentially two methods by which social choices can be made, voting, ... and the market mechanism": the second uses a measure, price expressed in terms of money. A measure or grade is a message that has strictly nothing to do with a utility. It provides a common language - be it numerical, ordinal or verbal - to grade and to classify. In this perspective, Arrow's theorem means that without a common language there can be no consistent collective decision. When the messages are grades expressed in a common language then one method of classifying competitors, candidates or alternatives - the majority-grade - and one method for ranking them|the majority-ranking - emerge as the only ones that satisfy each of various desirable properties. Together they are called the majority judgment. Related, they best resist strategic manipulations of judges and voters under varying assumptions concerning judges' and voters' ends and purposes. |
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University of Heidelberg Wednesday, July 11, 03:00, Session C Farsighted Coalitional Stability in TU-games [pdf] (joint work with Jacques Durieu, Philippe Solal) Abstract We study farsighted coalitional stability in the context of TU-games. Chwe (1994, p.318) notes that, in this context, it is difficult to prove nonemptiness of the largest consistent set. We show that every TU-game has a nonempty largest consistent set. Moreover, the proof of this result points out that each TU-game has a farsighted stable set. We go further by providing a characterization of the collection of farsighted stable sets in TU-games. We also show that the farsighted core of a TU-game is empty or is equal to the set of imputations of the game. Next, the relationships between the core and the largest consistent set are studied in superadditive TU-games and in clan games. In the last section, we explore the stability of the Shapley value. It is proved that the Shapley value of a superadditive TU-game is always a stable imputation: it is a core imputation or it constitutes a farsighted stable set. A necessary and sufficient condition for a superadditive TU-game to have the Shapley value in the largest consistent set is given. |
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University of Wisconsin - La Crosse Tuesday, July 10, 03:30, Session C Strategic Market Games with Cyclic Production [pdf] Abstract We consider an infinite horizon cash-in-advance market economy with symmetric agents. In each stage, a representative agent receives an independent, random endowment from one of k known distributions. The endowment distribution changes cyclically across stages. We suppose that a central bank sets a fixed, interest rate for both borrowing and investing. In equilibrium, the expected rate of inflation across each cycle of length k is strictly greater with random endowments from cyclic distributions than with deterministic endowments. |
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Carnegie Mellon University Thursday, July 12, 10:30, Session E A Theory of Risk Management with Applications to Executive Compensation and Earnings Management [pdf] Abstract This paper presents a theory of risk management in which the choices of managers over effort and risk are imperfectly monitored by outsiders. In a principal-agent framework, hedging can reduce extraneous noise in the variables outsiders observe or create opportunities for self-dealing behavior. The model reproduces several empirical features commonly described as anomalous, in an optimal-contract setting. In equilibrium, the hedged distribution of output is hump-shaped and asymmetric: first, for outputs close to the mode of the distribution, managers are more likely to do well and less likely to do poorly; second, managers hedge against large gains and increase the likelihood of large losses. The model accounts for the prevalence of linear compensation schemes and the relatively low performance-pay coefficients observed in managerial jobs. A simple linear contract is optimal over states with large payoffs or when the manager has access to all, or nearly all, fair hedges and gambles. In the latter case, the optimal contract may feature no observable performance-pay, yet elicit some effort. Empirical implications for the detection of earnings management, risk controls, robust contracting and observed compensation schemes across industries are also examined. |
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University of Glasgow Tuesday, July 10, 11:00, Session D Higher Education Admission in Hungary by a Score-limit Algorithm [pdf] Abstract The admission procedure of higher education institutions is organized by a centralized matching program in Hungary since 1985. We present the implemented algorithm, which is similar to the college-proposing version of the Gale-Shapley algorithm. The difference is that here ties must be handled, since applicants may have equal scores. The presented score-limit algorithm finds a solution that satisfies a special stability condition. We describe the applicant-proposing version of the above algorithm and we prove that the obtained solutions by these algorithms are the maximal and the minimal stable score-limits, respectively. |
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Microsoft Research Tuesday, July 10, 11:00, Session C Conversion Rates in Auctions for Sponsored Search [pdf] (joint work with Jason D. Hartline) Abstract The generalized second-price auction (GSP) is used predominantly for sponsored search in search engines like Google, MSN-Live Search and Yahoo!. It has been shown by Edelman, Ostrovsky and Schwarz (2006) and by Varian (2006) that GSP possesses an efficient pure Nash equilibrium. The model studied in Edelman et al and Varian assumed that all the clicks on the search engine ads gain the advertiser the same benefit. In practice, when an ad can be shown in one of several positions (a.k.a., slots) on the search results page, often the lower slots have higher acquisition rates. We study the implications of relaxing the identical acquisition rate assumption for GSP. In this case, we show that GSP does not always admit an efficient equilibrium anymore (neither pure nor mixed), even in the special case where ordering the advertisers by bid remains optimal. We show that when the bid space is discrete, an (inefficient) pure Nash equilibrium always exists, and we characterize the equilibria as a function of the parameters of the bidders' preferences. Finally, we quantify the inefficiency of these equilibria. |
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University of Warwick (UK) Tuesday, July 10, 03:55, Session B Elections and the Quality of Politicians [pdf] Abstract This paper concerns the nature of the candidate selection process in politics. The issue at hand is to understand how the competence of candidates and elected politicians is affected by ideological and partisan concerns. I analyze a two-party system with exogenous policies and endogenous candidacy. Citizens are heterogeneous with respect to ideology and competence and vote according to both of these dimensions. When a population is ideologically equilibrated between 'left' and 'right', there is a weak positive effect of politicians' pay and victory rent on the competence of the elected politician, regardless of the ideological concerns involved, and the limited amount of information on candidate quality available to voters. Unsurprisingly, a population that is ideologically very partisan would elect a consonant, but incompetent politician. Nevertheless, in the more general case, with a mildly partisan population, the discernment of candidate ability becomes less perfect and the election's result uncertain: the pay of politicians and the victory rent cease to have a linear effect on the quality of politicians. |
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New York University Wednesday, July 11, 11:00, Session B Divide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Procedure [pdf] (joint work with Michael A. Jones, Christian Klamler) Abstract Properties of discrete cake-cutting procedures that use a minimal number of cuts (n – 1 if there are n players) are analyzed. None is always envy-free or efficient, but divide-and-conquer (D&C) minimizes the maximum number of players that any single player may envy. It works by asking n >= 2 players successively to place marks on a cake that divide it into equal or approximately equal halves, then halves of these halves, and so on. Among other properties, D&C (i) ensures players of more than 1/n shares if their marks are different and (ii) is strategyproof for risk-averse players. However, D&C may not allow players to obtain proportional, connected pieces if they have unequal entitlements. Possible applications of D&C to land division are briefly discussed. |
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Ibmec Sao Paulo Tuesday, July 10, 03:55, Session C Heterogeneity of Central Bankers and Inflationary Pressure [pdf] (joint work with Fabia Carvalho) Abstract This paper investigates the role of the degree of heterogeneity of central bankers’ preferences in the output-inflation tradeoff. It builds a game theoretic model of monetary policy with inflation targets not set by the monetary authority and with uncertainty about the preferences of the central banker. Under reasonable assumptions, the model shows that in countries with greater dispersion in the distribution of central bankers’ preferences, as it is the case in a number of developing nations, monetary policy has to be tougher to convince society of the central banker’s commitment to controlling inflation. The model also shows that inflation targets have a role in anchoring expectations even when the central banker highly values output expansions. The paper also presents empirical evidence supporting the model’s results. |
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Georgia Tech Tuesday, July 10, 03:00, Session D The Computational Aspect of Risk in Playing Non-Cooperative Games Abstract This paper considers the computational aspect of risk in game playing situations. The risk we consider arises due to the players being compelled to choose mixed strategies in order to ensure that they play at a strategic equilibrium, which happens often when the game has no pure strategic equilibria. More precisely, this paper studies the following question: What is the computational complexity of finding equilibrium or near-equilibrium points where the risks of a given set of players are within specified bounds? |
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University of Wisconsin - Madison Friday, July 13, 03:30, Session C Belief-Based Strategies in the Repeated Prisoners’ Dilemma with Asymmetric Private Monitorin [pdf] Abstract The belief-based approach studies an important class of strategies for repeated games with private monitoring where at each point of the game, each player's optimal continuation strategy is determined by the player's beliefs of the private state of the opponents. This paper extends the belief-based approach to the repeated prisoners' dilemma with asymmetric private monitoring technologies. We first find that the previous type of construction in Sekiguchi (1997) and Bhaskar and Obara (2002) may not be sufficient to accommodate all asymmetric private monitoring scenarios, especially when players' private monitoring technologies are sufficiently di¤erent. We then modify the previous belief-based strategies by letting the player with smaller observation errors always randomize between "cooperate" and "defect" along the cooperative path of the play. It is shown that full efficiency can be approximated using a modified belief-based strategy profile, provided that observation errors are small and a public randomization device is available. We further construct a complete example to show that the modified beliefased strategies can be potentially generalized to other two-player repeated games with almost-perfect private monitoring structures. |
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Arizona State University Monday, July 9, 03:30, Session C Partially-informed Decision Makers in Games of Communication [pdf] Abstract We incorporate partially informed decision makers into games of communication through cheap talk. We analyze three different extensive-form games in which the expert and the decision maker (DM) privately observe signals about the state of the world. In game 1, the DM reveals her private signal to the expert before the expert reports to her. In game 2, the DM keeping her signal private while the expert reports to her. In game 3, the DM strategically communicates to the expert first before the expert reports to her. We find that the DM's expected equilibrium payoff is not monotonically increasing in the informativeness of her private signal because the expert may reveal less of his information when facing a better-informed DM. Whether the DM extracts more information from the expert in game 1 or in game 2 depends on the parameters. Allowing the DM to communicate strategically to the expert first does not help her extract more information from the expert. |
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Northwestern University Thursday, July 12, 10:30, Session B Belief Operator in a Universal Space [pdf] (joint work with Xiao Luo) Abstract In complex informational and strategic situations where individual(s)may exhibit very general preferences, we apply Morris’s (JET 69 (1996) 1-23) alternative notion of belief to the universal state space constructed by Epstein and Wang (Econometrica 64 (1996) 1343-1373), and study the logical properties of belief from a decision-theoretic point of view. |
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Pennsylvania State University Friday, July 13, 03:00, Session C Cooperation in the Repeated Prisoner's Dilemma Game with Local Interaction and Local Communication [pdf] Abstract The paper considers the repeated prisoner's dilemma game under a network where each agent interacts with his neighbors and he cannot observe the actions of others who are not directly connected to him. In this setting, when agents are sufficiently patient and the loss from being cheated is small enough, a trigger strategy that observing a deviation causes a permanent punishment cannot be a sequential equilibrium. Also, although the modification of the trigger strategy, following Ellison (1994), can be a sequential equilibrium supporting cooperation, it is not stable to mistakes in the sense that a mistake to play defection causes that all agents play defection forever. In this paper, we allow agents to communicate with their neighbors and construct a sequential equilibrium which supports cooperation and is stable to mistakes when the discount factor is high enough. Here, the role of local communication is to enable agent to resolve the discrepancy of his neighbors' beliefs on the punishment periods. |
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UCL Common Learning [pdf] (joint work with Ely, Mailath, Samuelson) Abstract Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily agents. Does it follow that the agents will commonly learn its value, i.e., that the true value of the parameter will become (approximate) common-knowledge? We show that the answer is affirmative when each agent’s signal space is finite and show by example that common learning can fail when observations come from a countably infinite signal space. |
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Laval University Thursday, July 12, 11:00, Session E Would Letting People Vote for Several Candidates Yield Policy Moderation? [pdf] Abstract We investigate whether letting citizens vote for several candidates would yield policy moderation compared to Plurality Voting. We do so in a setting that takes three key features of elections into account, namely, strategic voting, strategic candidacy and policy motivation on the part of the candidates. We consider two classes of voting rules. One class consists of the voting rules where each voter casts several equally-weighed votes for the different candidates. The other class consists of the voting rules where each voter rank-orders the different candidates. We then identify conditions under which those voting procedures yield policy moderation compared to Plurality Voting. We also show that if any one of those conditions is not satisfied, replacing Plurality Voting with one of those voting procedures may then yield policy extremism! Finally, we find that amongst those voting procedures the extent of policy moderation is maximal under Approval Voting and the Borda Count. Which of these two voting procedures yields the most moderate policy outcomes depends on (1) the symmetry of policy preferences, and (2) the presence of spoiler candidates. |
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Paris-Jourdan Sciences Économiques On the Influence of Rankings Abstract Ranking systems are becoming increasingly important in the academic world. By providing information on the quality of departments, journals, academics, their basic purpose is to help individuals or entities to make decisions. Hopefully they improve student's choice and researchers work and facilitate hiring and promoting procedures. They also shape incentives and preferences. I first review some of the justifications for the most prominently used methods. Then I propose a critical point of view by studying some dynamics these rankings may induce. |
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Paris-Jourdan Sciences Économiques Wednesday, July 11, 10:30, Session C Sharing Information in Web Communities [pdf] Abstract The paper investigates information sharing communities. The environment is characterized by the anonymity of the contributors and users, as on the Web. It is argued that a community may be worth forming because it facilitates the interpretation and understanding of the posted information. The admission within a community and the stability of multiple communities are examined when individuals differ in their tastes. |
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PSE-University of Paris I Price Dynamics on a Stock Market with Asymmetric Information [pdf] Abstract The appearance of a Brownian term in the price dynamics on a stock market was interpreted in [De Meyer, Moussa-Saley (2003)] as a consequence of the informational asymmetries between agents. To take benefit of their private information without revealing it to fast, the informed agents have to introduce a noise on their actions, and all these noises introduced in the day after day transactions for strategic reasons will aggregate in a Brownian Motion. We prove in the present paper that this kind of argument leads not only to the appearance of the Brownian motion, but it also narrows the class of the price dynamics: the price process will be, as defined in this paper, a continuous martingale of maximal variation. This class of dynamics contains in particular Black and Scholes' as well as Bachelier's dynamics. The main result in this paper is that this class is quite universal and independent of a particular model: the informed agent can choose the speed of revelation of his private information. He determines in this way the posterior martingale L, where L_q is the expected value of an asset at stage q given the information of the uninformed agents. The payoff of the informed agent at stage q can typically be expressed as a 1-homogeneous function M of L_{q+1}-L_{q}. In a game with n stages, the informed agent will therefore chose the martingale L^n that maximizes the M-variation. Under a mere continuity hypothesis on M, we prove in this paper that L^n will converge to a continuous martingale of maximal variation. This limit is independent of M. |
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Vanderbilt University Monday, July 9, 10:30, Session A Monopoly and Oligopoly Supply of a Durable Good with Network Externalities [pdf] Abstract This paper models a good for which there are dynamic network externalities, and investigates the properties of the Markov Perfect equilibrium (MPE) that arises when there is monopoly or oligopoly supply. The framework is a continuous-time overlapping-generations model with constant- probability- of- death in which every member of a cohort born at some time t must make a once-and-for-all decision as to whether to purchase a good which enhances such a member's income. Each cohort is heterogeneous in regards to the e¤ect of this good on an individual’s earnings. Furthermore, the enhancement of earnings at every moment depends on how many other people at that time also possess the good. Hence, each member of a cohort faces the problem of forecasting how many people in the future will purchase the good. Key results are that positive network externalities may lead to steady-state price less than marginal cost, disadvantageous market power, and multiple equilibria (only one of which is the limit of a fnite-horizon solution). |
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The Hebrew University Wednesday, July 11, 11:00, Session D The Mertens and Neyman Values of Non-differentiable Vector Measure Games [pdf] Abstract
The concept of a value for a game with a continuum of players was introduced by Aumann and Shapley in [AS]. The Mertens value defined in [Me] and the Neyman value defined in [Ne] are two values defined over large spaces containing "non-differentiable" games with a continuum of players. Neyman proved in [Ne] that the two values coincide on games of the form $f(u)$ where f is concave and u is a vector measure; It was the asked (in [Ne]) if the values coincide on some subsets of a large set of vector measure games Q. We study this question and explore the behavior of these values. We also adopt a new perspective of the Neyman value as an "approximate smoothing value" and prove a very general "diagonal formula" which extends the formula derived in section 6.1 of [Ne]. |
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Northwestern University Critical Types (joint work with Marcin Peski) Abstract
Economic models employ assumptions about agents' infinite hierarchies of belief. We might hope to achieve reasonable approximations by specifying only finitely many levels in the hierarchy. However, it is well known since Rubinstein(1989) that the behaviors of some fully specified hierarchies can be very different from the behavior of such finite approximations. Examples and earlier results in the literature suggest that these critical types are characterized by some strong assumptions on higher-order beliefs. We formalize this connection. We define a critical type to be any hierarchy at which the rationalizable correspondence exhibits a discontinuity. We show that critical types are precisely those types for which there is common belief in a certain class of event. We discuss why nearly all types in commonly-used applied models are critical types. On the other hand, we show that regular types, i.e. types which exhibit no discontinuities, are generic. In particular they form a residual set in the product topology. This second result strengthens a previous one due to Weinstein and Yildiz (2006) in two ways. First, while Weinstein and Yildiz (2006) considered a fixed game, our regular types have continuous behavior across all games. |
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Lund University Tuesday, July 10, 10:00, Session E The Role of Observational Skill in Coordination Games [pdf] Abstract
A M × M coordination game is analyzed in an evolutionary environment. Agents are assumed to be able to make noisy observations of opponent’s behavior, called reputation, and form preferences over opponents based on their reputation. The both strategies and observational skills in the population are subjected to a constant level of perturbations. A game takes place when two agents agree to play. It has been show in previous studies that perfect observational skill leads to an efficient outcome. However this result is ultimately dependent on how well agents can observe their feasible opponents. In this paper we endogenize observational skill. We show how evolutionary pressure improves observational skill endogenously. We find that evolutionary forces will bring the population to a point where all agents have perfect observational skill and play the efficient strategy. In a more realistic setting where cost is strictly increasing in observational skill, we find that there exist cost functions leading to a state where agents can observe the opponents reputation sufficiently well which in turn result in an efficient outcome. In the general 2 × 2 case, we show that a fixed cost function results in partition such that the set containing games with a significantly risk dominant strategy converge to the risk-dominant equilibrium whereas all other games converge to the efficient equilibrium. Furthermore, the observational skill will regress as the population converges to equilibrium. |
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Stanford University Monday, July 9, 03:30, Session D Cooperation and Self-Governance in Heterogeneous Communities [pdf] Abstract This paper theoretically studies the consequences of unobservable heterogeneity on self-governance and cooperation in large communities. I consider a game model where players belong to a large population and are randomly matched. Players interact with each other infrequently and, when matched, play a prisoners' dilemma. There exists an institution that can convey information on play histories. Players' payoff functions differ, so that some players have a higher tendency towards cooperation. This constitutes the main modeling innovation of this work and makes the model a mixed adverse selection-moral hazard model. A suitable equilibrium concept is introduced and characterized. Some novel comparative statics results are obtained; showing in particular that more heterogeneous societies may sustain more cooperation. Decentralization and stability analyses are carried out. Private enforcement mechanisms are explored, showing conditions under which private intermediation leads to Pareto optimal cooperation. Applications and examples are explored. |
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New York University Thursday, July 12, 10:00, Session D Behavioral Equilibrium in Economies with Adverse Selection [pdf] Abstract I propose a new solution concept, behavioral equilibrium, to study environments with players who are naive in the sense that they fail to account for the informational content of other players' actions. A behavioral equilibrium requires that: (i) players have no incentives to deviate given their beliefs about the consequences of deviating, (ii) these beliefs are consistent with the information obtained from the actual equilibrium play of all players, and (iii) when processing this information, naive players fail to account for the correlation between other players' actions and their own payoff uncertainty. I apply the framework to certain adverse selection settings and show that, contrary to the received literature, the adverse selection problem is exacerbated when naive players fail to account for selection. More generally, the main distinguishing feature of the framework is that in equilibrium beliefs about both fundamentals and strategies are jointly restricted. Consequently, whether a bias may arise or not is determined endogenously in equilibrium. |
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Yale University Friday, July 13, 03:00, Session E Reputation Effects and Equilibrium Degeneracy [pdf] (joint work with Yuliy Sannikov) Abstract We study a continuous-time reputation game between a large player and a population of small players in which the actions of the large player are imperfectly observable. The small players believe that the large player could be either a strategic normal type or a commitment type, who plays the same action at all times. We characterize the sequential equilibrium correspondence in terms of a two-point boundary value problem for a differential equation. We provide a sufficient condition for the sequential equilibrium to be unique and Markov in the small players’ posterior belief. A side product of our characterization is that when the small players are certain that they are facing the normal type, the set of equilibrium payoffs of the large player coincides with the convex hull of the set of static Nash equilibrium payoffs. |
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Prism Analytics / Russell Investment Group / DePaul University Friday, July 13, 03:00, Session A A Theory of Attribution [pdf] Abstract
Attribution of economic joint effects is achieved with a random order model of their relative importance. Random order consistency and elementary axioms uniquely identify linear and proportional marginal attribution. These are the Shapley (1953) and proportional (Feldman (1999, 2002) and Ortmann (2000)) values of the dual of the implied cooperative game. Random order consistency does not use a reduced game. Restricted potentials facilitate identification of proportional value derivatives and coalition formation results. Attributions of econometric model performance, using data from Fair (1978), show stability across models. Proportional marginal attribution (PMA) is found to correctly identify factor relative importance and to have a role in model construction. A portfolio attribution example illuminates basic issues regarding utility attribution and demonstrates investment applications. PMA is also shown to mitigate concerns (e.g., Thomas (1977)) regarding strategic behavior induced by linear cost attribution. |
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Northwestern University Monday, July 9, 11:00, Session A Using Aftermarket Power to Soften Foremarket Competition [pdf] Abstract This paper studies competition among equipment sellers who each monopolize their equipment's aftermarket. However, their aftermarket power is contested by foremarket competition as equipment owners view new equipment as a substitute for their incumbent firm's aftermarket product. I show that such constrained aftermarket power allows a larger number of firms to sustain the monopoly profits. More strikingly, as long as existing customers have a shorter market life expectancy than incoming customers, for any discount factor, supranormal profits are sustainable among arbitrarily many firms each selling ex ante identical products. Ironically, if the aftermarket is isolated from foremarket competition, then aftermarket power no longer facilitates tacit collusion, suggesting the importance of distinguishing between two types of aftermarket power which are often considered to be qualitatively the same. |
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University of California, Berkeley Topological Games at Princeton (and after) Abstract The games of the title are "Nash" (or Hex), "Milnor" (or Y), "Shapley" (or Projective Plane) and "Gale" (or Bridg-It) all of which were discovered (or re-discovered) in Princeton in 1948-49. After giving the basic topological connections I will discuss more recent ramifications related to computational complexity theory and renormalization. A recurrent theme will be non-constructive proofs, or how we can know something can be done without having the slightest idea of how to do it. |
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Cornell University Thursday, July 12, 11:00, Session B Common P-belief and Uncertainty [pdf] Abstract This paper generalizes the notion of common p-beliefs to situations of ambiguity or Knightian uncertainty. When players have multiple prior beliefs,we show that Aumann's no-agreement theorem can be approximated. We also provide conditions under which purely speculative trade does not occur in the presence of ambiguity when players preferences are complete or incomplete. |
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ISEG Universidade Tecnica de Lisboa Monday, July 9, 03:00, Session E Endogenous Heterogeneity in Strategic Models: Further Results [pdf] (joint work with Rabah Amir, Malgorzata Knauff) Abstract This paper is an attempt to develop a unified approach to endogenous heterogeneity by constructing general class of two-player symmetric games that always possess only asymmetric pure-strategy Nash equilibria. These classes of games are characterized in some abstract sense by two general properties: payoff non-concavities and some form of strategic substitutability. We provide a detailed discussion of the relationship of this work with Matsuyama's symmetry breaking framework and with business strategy literature. Our framework generalizes a number of models dealing with two-stage games, with long term investment decisions in the first stage and product market competition in the second stage. We present the main examples that motivate this study to illustrate the generality of our approach. |
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Yale University Social Memory and Evidence from the Past [pdf] (joint work with Luca Anderlini and Roger Lagunoff) Abstract Examples of repeated destructive behavior abound throughout the history of human societies. This paper examines the role of social memory - a society's vicarious beliefs about the past - in creating and perpetuating destructive conflicts. We examine whether such behavior is consistent with the theory of rational strategic behavior. We analyze an infinite-horizon model in which two countries face off each period in an extended Prisoner's Dilemma game in which an additional possibility of mutually destructive “all out war” yields catastrophic consequence for both sides. Each country is inhabited by a dynastic sequence of individuals who care about future individuals in the same country, and can communicate with the next generation of their countrymen using private messages. The two countries' actions in each period also produce physical evidence; a sequence of informative but imperfect public signals that can be observed by all current and future individuals. We find that, provided the future is sufficiently important for all individuals, regardless of the precision of physical evidence from the past there is an equilibrium of the model in which the two countries' social memory is systematically wrong, and in which the two countries engage in all out war with arbitrarily high frequency. Surprisingly, we find that degrading the quality of information that individuals have about current decisions may “improve” social memory so that it can no longer be systematically wrong. This in turn ensures that arbitrarily frequent all out wars cannot take place. |
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Dartmouth College Friday, July 13, 03:00, Session B Two Experts are Better than One [pdf] Abstract This paper proposes a communication mechanism between a receiver and two senders who are perfectly informed about the state of nature, and biased in the same direction. We show that by threatening to recur to his prior beliefs when receiving conflicting messages from two senders simultaneously, the receiver can render the disclosure mechanism more informative, compared to only consulting the less biased sender. The findings are robust to a wide range of informative bias combinations and differ from the results of the literature on sequential disclosure. In particular, this paper offers a novel rejoinder to the work of Krishna and Morgan (QJE, 2001), who show that a receiver is typically worse off when adding a second, more biased sender. Our mechanism is not only more informative compared to KM’s solution, it is also more informative than the original equilibrium concept in Crawford and Sobel (Econometrica, 1982). Multisender cheap-talk mechanisms under simultaneous disclosure are commonly used in real-life organizations. Many organizations from the business world to media deal with the problem of combining the expertise rooted in the knowledge of more than one sender, and use the presence of a second sender when the two senders are known to disagree when specific states of nature are observed. Such settings in mind, this paper studies some of the design options that simultaneous disclosure games offer to refine the strategy profile. The equilibrium concept studied in this paper departs from the analysis in Krishna and Morgan (2001) in that it drops the assumption of two experts being unaware of each other’s existence. While Krishna and Morgan already refer to the option of directly combining break points of two Crawford-Sobel disclosure profiles as the “coarsest common refinement,” we use a different way to combine two simultaneously disclosed messages in a unidimensional setting. The paper offers a description of the two-sender disclosure mechanism, defines the equilibrium concept, and generalizes the setting by both discussing possible bias combinations that follow from the Crawford-Sobel game, and by offering other extensions that further illustrate the receiver's commitment to refuse expertise altogether when the experts disagree. |
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Carnegie Mellon University Monday, July 9, 10:30, Session C Gradient-based Algorithms for Finding Nash Equilibria in Extensive Form Games [pdf] (joint work with Samid Hoda, Javier Pena, Tuomas Sandholm) Abstract We present a computational approach to the saddle-point formulation for the Nash equilibria of two-person, zero-sum sequential games of imperfect information. The algorithm is a first-order gradient method based on modern smoothing techniques for non-smooth convex optimization. The algorithm requires O(1/epsilon) iterations to compute an epsilon-equilibrium, and the work per iteration is extremely low. These features enable us to find approximate Nash equilibria for sequential games with a tree representation of about 10^{10} nodes. This is three orders of magnitude larger than what previous algorithms can handle. We present two heuristic improvements to the basic algorithm and demonstrate their efficacy on a range of real-world games. Furthermore, we demonstrate how the algorithm can be customized to a specific class of problems with enormous memory savings. |
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University of Montreal Monday, July 9, 03:00, Session C Informative Cheap Talk Equilibria as Fixed Points [pdf] Abstract We introduce a new fixed point method to analyze cheap talk games, in the tradition of Crawford and Sobel (1982). We illustrate it in a class of onedimensional games, where the sender’s bias may depend on the state of the world, and which contains Crawford and Sobel’s model as a special case. The method yields new results on the structure of the equilibrium set. For games in which the sender has an outward bias, i.e. the sender is more extreme than the receiver whenever the state of the world is extreme, we prove that for any positive integer k, there is an equilibrium with exactly k pools, and at least one equilibrium with an infinite number of pools. We discuss the extent to which the fixed point method can be used to address other cheap talk signalling problems. |
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Duke University Tuesday, July 10, 03:30, Session D Improved VCG Redistribution Mechanisms [pdf] (joint work with Vincent Conitzer) Abstract For resource allocation problems with free disposal, the Vickrey-Clarke-Groves (VCG) mechanism is efficient (it allocates the items to maximize total value), strategy-proof (agents have no incentive to lie about their valuations), individually rational (participating in the mechanism never hurts), and does not incur a deficit (the agents' payments sum to at least 0). However, the VCG mechanism is not (strongly) budget balanced: generally, the agents' payments will sum to more than 0. This decreases agents' utilities. In 2006, Cavallo proposed a mechanism that redistributes some of the VCG payments back to the agents, while maintaining the other properties. We investigate whether better redistribution mechanisms exist. We first study settings where there are multiple indistinguishable units of a single good, and each agent wants at most one unit. We propose a mechanism (WCO) that maximizes the worst-case redistribution percentage. This mechanism belongs to the class of linear redistribution mechanisms, and among these it is in fact the unique worst-case optimal mechanism. (In a 2007 working paper, Moulin has independently derived the same mechanism, as the result of a different optimization problem.) The optimal mechanism remains the same even if the individual rationality constraint is dropped. (This is not true in Moulin's setting.) For general settings (not necessarily unit demand), we propose several techniques that take a redistribution mechanism as input, and produce as output a mechanism that always redistributes at least as much to every agent -- that is, the new redistribution mechanism dominates the old one. One of our techniques immediately produces an undominated mechanism; the other does not, but iterative application of the technique results in an undominated mechanism in the limit. We apply these techniques to both Cavallo's mechanism and the WCO mechanism. The resulting mechanisms redistribute significantly more. |
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Ben-Gurion University Monday, July 9, 11:00, Session D On the Existence of Bayesian Cournot Equilibrium [pdf] (joint work with Ezra Einy, Diego Moreno, Benyamin Shitovitz) Abstract We show that even in very simple oligopolies with differential information a (Bayesian) Cournot equilibrium in pure strategies may not exist, or be unique. However, we find sufficient conditions for existence, and for uniqueness, of Cournot equilibrium in a certain class of industries. More general results arise when negative prices are allowed. |
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Harvard Business School Tuesday, July 10, 10:30, Session D Unravelling in Two-Sided Matching Markets and Similarity of Preferences [pdf] Abstract This paper investigates the causes and welfare consequences of unravelling in two-sided matching markets. It shows that similarity of preferences is an important factor driving unravelling. In particular, it shows that under the ex-post stable mechanism (which is the mechanism the literature focuses on), unravelling is more likely to occur for more similar preferences. Moreover, it shows that any Pareto-optimal mechanism must prevent unravelling, and that the ex-post stable mechanism is Pareto-optimal if and only if it prevents unravelling. |
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Hebrew University of Jerusalem An Operational Measure of Riskiness (joint work with Dean P. Foster) Abstract We define the riskiness of a gamble g as that unique number R(g) such that no-bankruptcy is guaranteed if and only if one never accepts gambles whose riskiness exceeds the current wealth. |
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The Ohio State University Friday, July 13, 03:30, Session E Group Reputations, Stereotypes, and Cooperation in Repeated Games [pdf] Abstract Reputation effects and other-regarding preferences have each been used to predict cooperative outcomes in markets with inefficient equilibria. Existing reputation-building models require either infinite time horizons or publicly observed identities, but cooperative outcomes have been observed in several moral hazard experiments with finite horizons and anonymous interactions. This paper introduces a full reputation equilibrium(FRE) with stereotyping (perceived type correlation) in which cooperation is predicted in early periods of a finitely repeated market with anonymous interactions. New experiments generate results in line with the FRE prediction, including final-period reversions to stage-game equilibrium and non-cooperative play under unfavorable payoff parameters. |
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The Open University of Israel Game States Abstract In dynamic interactions involving mutual unawareness regarding the structure of the game, the concept of a strategy is questionable. Game states constitute a framework for defining solution concepts based on rationality and mutual belief of rationality of actions rather than strategies. For a given extensive-form game, a game state specifies a node n, the active players' choice of actions in that node, these players' beliefs about game states, and the game state that would obtain in every other node n'. Consistency conditions govern the mappings from game states to beliefs and to the game states that would obtain in alternative nodes. An action of a player at a node is rationalizable if it is taken in some game state that belongs to a maximal set of events expressing optimality of actions in nodes and mutual belief of optimality. Assuming also common knowledge of these actions pins down a subset of the rationalizable actions. We demonstrate the usefulness of these concepts in several examples. |
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KSM-MEDS, Northwestern Private Monitoring without Conditional Independence (joint work with Kyna Fong, Olivier Gossner, Yuliy Sannikov) Abstract We prove the existence of sequential equilibria that approximately achieve the efficient payoff in the infinitely repeated two-player prisoner's dilemma under low discounting with imperfect private monitoring. We impose a lower bound on the informativeness of the signals, but we do not require almost-perfect monitoring or conditional independence. |
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Soochow University Wednesday, July 11, 10:00, Session D The Potential and Consistency Property for Multi-choice Shapley Value (joint work with Yu-Hsien Liao) Abstract In 1991, when Hsiao and Raghavan presented [3] in the 2rd International Conference on Game Theory at Stony-Brook, Shapley suggested that we should study the consistent property of the H&R Shapley value. In this article, we characterize the extended Shapley value proposed by Hsiao and Raghavan [2, 3]. We complete the proof that the extended Shapley value has w-consistent property proposed by Hsiao, Yeh and Mo [4]. Then we provide an axiomatization which is the parallel of Hart and Mas-Colell's [1] axiomatization of the Shapley value by applying the w-consistency property. |
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Pennsylvania State University Tuesday, July 10, 10:30, Session B Logic for Games of Perfect Information and Epistemic Conditions for Backward Induction and Subgame Perfectness [pdf] Abstract We propose a logical system in which a notion of the structure of a game is formally defined and the meaning of sequential rationality is formulated. We provide a set of decision criteria which, given sufficiently high order of mutual belief of the game structure and of every player following these criteria, entails Backward Induction decisions in generic perfect information games. We say that a player is rational if the player follows these criteria in his/her decisions. The set of mutual beliefs is also necessary, in the sense that any mutual belief of lower order can not entail the Backward Induction decisions. These conditions are determined by the length of the game structure, and they are never involved with common belief. Moreover, we give a set of epistemic conditions for subgame perfect equilibria for any perfect information game, which requires every player follow these decision criteria and there be mutual belief of the the equilibrium strategy and of the game structure. |
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University of the Basque Country Monday, July 9, 11:00, Session B The Stability of the Roommate Problem Revisited [pdf] (joint work with C. Larrea, E. Molis) Abstract
The purpose of this paper is to determine the absorbing sets, a solution that generalizes the notion of (core) stability, for the entire class of the roommate problems with strict preferences. |
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IBM TJ Watson Research Centrer Thursday, July 12, 10:30, Session C A Design for an Asymptotically Efficient Combinatorial Bayesian Market: Generalizing the Satterthwaite-Williams Mechanism [pdf] (joint work with Pravin Varaiya) Abstract
We consider the problem of efficient mechanism design for multilateral trading of multiple goods with independent private types for players and incomplete information among them. The problem is partly motivated by an efficient resource allocation problem in communication networks where there are both buyers and sellers. In such a setting, ex post budget balance and individual rationality are key requirements, while efficiency and incentive compatibility are desirable goals. Such mechanisms are difficult if not impossible to design. We propose a combinatorial market mechanism which in the complete information case is efficient, budget-balanced, ex post individual rational and "almost" dominant strategy incentive compatible. In the incomplete information case, it is budget-balanced, ex post individual rational and asymptotically efficient and Bayesian incentive compatible. Thus, we are able to achieve efficiency, budget-balance and individual rationality by compromising on incentive compatibility. The mechanism may be considered a variation on the generalized Satterthwaite-Williams mechanism. |
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Rice University Wednesday, July 11, 10:30, Session B Group strategyproof cost sharing: the role of indifferences [pdf] Abstract Every agent reports his willingness to pay for one unit of good. A mechanism allocates some goods and cost shares to some agents. A tie-breaking rule describes the behavior of an agent who is offered a price equal to his valuation. We characterize the group strategyproof (GSP) mechanisms under two alternative tie-breaking rules. With the maximalist rule (MAX) an indifferent agent is always served. With the minimalist rule (MIN) an indifferent agent does not get a unit of good. GSP and MAX characterize the population-monotonic mechanisms. These mechanisms are appropriate for submodular cost functions. On the other hand, GSP and MIN characterize the sequential mechanisms. These mechanisms are appropriate for supermodular cost functions.Our results are independent of an underlying cost function; they unify and strengthen earlier results for particular classes of cost functions. |
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University of Tokyo Thursday, July 12, 10:00, Session C A Strategic Theory of Markets [pdf] Abstract A strategic theory of the market investigates existence of an equilibrium, price formation, and design of a trading procedure in an environment where each player has private information and can significantly affect the market outcome.In this paper we evaluate the performance of a double auction in a multi-unit exchange economy with affiliated values. Our first result shows (by approximating the market with a continuum of players) that there exists a pure strategy equilibrium in nondecreasing strategies when there are sufficiently many players. The second result is a equilibrium pricing function converges to the fully revealing rational expectation equilibrium as the number of players increases. One implication of our analysis is that distribution of information among players can have significant implications on the validity of efficient market hypothesis and performance of trading procedures even when players are fully rational and share common knowledge of the economic environment and the trading procedure. |
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The Hebrew University of Jerusalem Wednesday, July 11, 10:00, Session E On Public Opinion Polls and Voters' Turnout [pdf] (joint work with Eyal Winter) Abstract This paper studies the effects that the revelation of information on the electorate's preferences has on voters' turnout decisions. The experimental data show that closeness in the division of preferences induces a significant increase in turnout. Moreover, for closely divided electorates (and only for these electorates) the provision of information significantly raises the participation of subjects supporting the slightly larger team relative to the minority team. This behavior contradicts the qualitative predictions of the unique quasi-symmetric Nash equilibrium of the theoretical model. We show that the heterogeneous effect of information on the participation of subjects in different teams is driven by the subjects' (incorrect) beliefs of casting a pivotal vote. Simply put, subjects overstate the probability of casting a pivotal vote when they belong to the team with a slight majority, and choose the strategy that maximizes their utility based on their inflated probability assessment. Empirical evidence on gubernatorial elections in the US between 1990 and 2005 is consistent with our main experimental result. Namely, we observe that the difference in the actual vote tally between the party leading according to the polls and the other party is larger than the one predicted by the polls only in closely divided electorates. |
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University of Oregon Monday, July 9, 11:00, Session C Endogenous Sharing Rules with Atomic and Nonatomic Players: Application to Subgame Perfection Abstract This paper examines discontinuous games between atomic and nonatomic players in the presence of endogenous sharing rules and extends equilibrium existence results of Simon and Zame (Econometrica 1990) to this framework. These results are in turn used to establish subgame perfect equilibrium existence in continuous strategy multi-stage games between atomic and nonatomic players. |
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Kellogg School of Management Tuesday, July 10, 10:30, Session E On the Elimination of Dominated Strategies in Stochastic Models of Evolution with Large Populations [pdf] Abstract
This paper analyzes a stochastic best reply evolutionary model with inertia in normal form games. The long-run behavior of individuals in this model is investigated in the limit where experimentation rates tend to zero, while the expected number of experimenters, and hence also population sizes, tend to infinity. Conditions on the learning-rate which are necessary and sufficient for the evolutionary elimination of weakly dominated strategies are found. The key determinant is found to be the sensitivity of the learning-rate to small payoff differences. |
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Crest-Insee Wednesday, July 11, 11:00, Session A Contingent Auctions with Allocative Externalities: Vickrey versus the Ausubel-Milgrom Proxy Auction [pdf] Abstract
We introduce contingent auction mechanisms, which is a superset of combinatorial auctions, and where bidders submit bids on packages that are contingent on the whole final assignment. Without externalities, the Vickrey and the Ausubel-Milgrom Proxy Auction are both robust if items are perceived as substitutes. Such an equivalence between those formats may not hold with externalities and the analog of the substitute condition is a complex unexplored issue. We analyse those issues in the Negative Group-Dependent Externalities framework, a general structure with allocative externalities between joint-purchasers. |
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Ecole Polytechnique and CNRS Tuesday, July 10, 03:00, Session E A New Theory of Social Choice [pdf] (joint work with Michel Balinski) Abstract The fundamental problem of the theory of social choice is to find a social decision function whose inputs are messages of judges or voters and whose outputs are the jury or electoral decisions, usually rank-orderings of competitors and winners.The traditional 700 year old model contains many impossibility theorems and pretends to aggregate the preferences (or utilites) of the judges or voters.In the real world, a judge's or a voter's preferences or utilities depends on a host of factors that include the decision (or output), the messages of the other judges (a judge or voter may wish to differ from the others, or on the contrary resemble the others), the social decision function that is used (a judge may prefer a decision given by"`democratic" function to one rendered by an "oligarchic" function, or the contrary) and the message he or she thinks is the right one (a judge may prefer honest behavior, or not). We contend that the deep preference functions of judges or voters cannot be the input of a practical model. A judge's input message is simply a message, nothing more and will depend on his complex utility function.Practice suggests a different formulation of the input messages. Olympic competitions in figure skating and gymnastics, wine competitions, competitions among pianists, flautists or orchestras, professors, all use measures or grades.This paper describes a new model for social choice and will develop certain of its properties. A subsequent talk by Michel Balinski will give an overview of the entire theory. |
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Chinese University of Hong Kong Tuesday, July 10, 11:00, Session B "Knowing Whether" and Unawareness [pdf] Abstract Unawareness, often interpreted as that one does not know an event, and he does not know that he does not know it, and so on ad infinitum, has important economic implications. However, as shown by Dekel, Lipman and Rustichini (1998, hereafter DLR), standard state-space models of information and knowledge cannot accommodate a plausible notion of unawareness. In this paper, we propose a different definition of unawareness, which is based on the "Knowing Whether" operator proposed by Hart, Heifetz and Samet (1996). Specifically, a person is unaware of an event if he does not know whether the event has occurred, and he does not know whether he knows whether the event has occurred, and so on ad infinitum. We modify DLR’s axioms accordingly, and find that nontrivial unawareness is possible in standard state-space models under the new formulation. Our examples also show that a non-partitional possibility correspondence does not necessarily accommodate unawareness. We identify a necessary and sufficient condition on the possibility correspondence, under which there exists nontrivial unawareness. |
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National Cheng Kung University, Tainan, TAIWAN Tuesday, July 10, 03:30, Session A Strategic Selection of Direct Selling and Private Brand in Retail Market under Retailer Stackelberg [pdf]
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