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Speakers**

Hebrew University of Jerusalem
People’s actions often deviate from rationality, i.e., self-interested behavior. We propose a paradigm called rule-rationality, according to which people do not maximize utility in each of their acts, but rather follow rules or modes of behavior that usually–but not always–maximize utility. Specifically, rather than choosing an act that maximizes utility among all possible acts in a given situation, people adopt rules that maximize average utility among all applicable rules, when the same rule is applied to many apparently similar situations. The distinction is analogous to that between Bentham’s “act-utilitarianism” and the “rule-utilitarianism” of Mill, Harsanyi, and others. The genesis of such behavior is examined, and examples are given. The paradigm may provide a synthesis between rationalistic neo-classical economic theory and behavioral economics. |

University of Pittsburgh
Different people use language in different ways. Private information about language competence can be used to reflect the idea that language is imperfectly shared. In optimal equilibria of common interest games there will generally be some benefit from communication with an imperfectly shared language, but the efficiency losses from private information about language competence in excess of those from limited competence itself may be significant. In optimal equilibria of common-interest sender-receiver games, private information about language competence distorts and drives a wedge between the indicative meanings of messages (the decision-relevant information indicated by those messages) and their imperative meanings (the actions induced by those messages). Indicative meanings are distorted because information about decision relevant information becomes confounded with information about the sender's language competence. Imperative meanings of messages become distorted because of the uncertain ability of the receiver to decode them. We show that distortions of meanings persist with higher-order failures of knowledge of language competence. In a richer class of games, where both senders and receivers move at the action stage and where payoffs violate a self-signaling condition, these distortions may result in complete communication failure for any finite-order knowledge of language competence. |

New York University
In many strategic settings with private information, optimality requires people to make hypothetical inferences about the information content of others' actions. We conduct an experiment under one such setting, a voting environment under private information, where optimality requires voters to extract information about others' information under the hypothetical event that their own vote is pivotal. We test for strategic behavior by means of an experimental design that distinguishes the mistake of failing to account for others' information from other mistakes that are natural in the process of drawing inferences from the pivotal event. Depending on the treatment, between 50% and 80% of our subjects fail to vote strategically. We find this mistake to be robust to experience and hints about pivotality, and to be mainly driven by the failure to make inferences from hypothetical, rather than actual, events. |

London School of Economics
(Joint work with Michele Piccione) We study a model of trading on a financial market with risk-neutral investors who can perform only limited short selling. Traders use "incomplete theories" that give statistically correct beliefs about the distribution of future prices conditional upon the information inside of their theories; they do not condition upon information conveyed by current prices. The more theories are present in the market, the higher is the equilibrium price of the risky asset, which always exceed the most optimistic trader's expectation of its present-discounted value. Prices may depend upon irrelevant information and become less informative about fundamentals as all traders use more complete theories. When dividends are persistent and interest rates constant, low asset prices are more volatile than high asset prices. Investors with more complete theories do not necessarily earn higher average returns than those with less complete theories. |

University College London and PSE
We consider a repeated interaction between a long run player and a sequence of short run players in which the long run player may either be rational or mechanical thereby always adopting the same stationary mixed strategy. The setup differs from Fudenberg and Levine's model in that the short run players are assumed to reason and make inferences by analogical reasoning, by which we mean that they understand the strategy of the various types of long run players only in aggregate over all time periods and histories after which the long run player may be called to play. A complete characterization is provided for the case in which the stage game involves two actions both for the long run and the short run player. It is shown that the rational long run player may get a payoff strictly larger than the payoff he would obtain if he were committed to play as the mechanical type of his choice, thereby enlarging the scope for reputation building in contexts with analogical reasoning. Various extensions are considered. |

Northwestern University
Harsanyi type spaces, the device traditionally used to model players' beliefs in games, generate infinite hierarchies of beliefs. Can the standard framework nevertheless be used to model situations in which players potentially have a finite depth of reasoning? This paper extends the Harsanyi framework to allow for higher-order uncertainty about players' depth of reasoning. The key idea is that players with a finite depth of reasoning cannot distinguish states that differ only in players' beliefs at high orders. Importantly, this approach makes clear that even if players have a limited depth of reasoning, they may still be able to reason about certain higher-order events. In particular, players with a finite depth of reasoning can have common knowledge of a nontrivial event, while they may not be able to reason about its complicated implications. The intuition is that common knowledge can be induced by simple public observations, while other forms of higher-order reasoning require much more sophistication. This has implications for the question what the relevant perturbations of higher-order beliefs are when examining the robustness of game-theoretic predictions. |

University College London
This paper provides a model of categorizations that are optimal for the purpose of making predictions. In the beginning of each period a subject observes a two-dimensional object in one dimension and wants to predict the object’s value in the other dimension. The subject uses a categorization that partitions the space of objects into categories. She has a data base of objects that were observed in both dimensions in the past. The subject determines what category the new object belongs to on the basis of observation of its first dimension. She predicts that its value in the second dimension will be equal to the average value among the past observations in the corresponding category. At the end of each period the second dimension is observed. The optimal categorization minimizes the expected prediction error. The main result is that the optimal number of categories is determined by a trade-off between (a) decreasing the size of categories in order to enhance category homogeneity, and (b) increasing the size of categories in order to enhance category sample size. |

University of Toronto
We analyze asynchronous repeated games with private and rich monitoring. We assume that strategies have finite past, i.e., in each period, continuation strategies must be measurable with respect to finite partitions of past histories. This class includes finite automata and bounded recall strategies. Additionally, we assume that the monitoring has an infinite number of signals. We show that any equilibrium with finite past and generic infinite monitoring has to satisfy a version of the belief-free property: in each period t, the set of best responses does not depend on the information received before period t, with a possible exception of the information received in the first periods of the game. Under an additional payoff smoothness assumption, the equilibrium strategy are essentially past-independent: each period's action depends only on the information received immediately prior to the choice of the action. |

Stern School of Business, New York University
In the term "bounded rationality," the word "bounded" is apparently an adjective modifying the work "rationality." In this talk I adopt the view that the term "bounded rationality" is concerned with how "smart" decision-makers deal with "bounded cognition," i.e., cognitive limitations that preclude fully rational procedures in the sense of (say) L. J. Savage. This is in the spirit of the work of H. A. Simon, J. Marschak, and also, to some extent, Savage himself. Thus I see the topic as a subfield, but only a proper subfield, of what has come to be called "behavioral economics" (or the equivalent in psychology and sociology). I shall here confine my attention to situations with a single decision-maker, leaving it to others in this conference to deal with games, markets, and evolution. After a brief review of the Savage paradigm, I review in that context the problems raised by various aspects of bounded cognition, and various suggested models of corresponding behavior. A few of these models seem promising as being relevant to some concept of "rationality," but none successfully addresses the cognitive limitation of the "failure of logical omniscience." For this reason, one may suspect that the locution "bounded rationality" is an oxymoron. |

Yale University
Axiomatic bargaining theory (e.g., Nash's theorem) is static. We attempt to provide a dynamic justification for the theory. Suppose a Judge or Arbitrator must allocate utility in an (infinite) sequence of two-person problems; at each date, the Judge is presented with a utility possibility set in the nonnegative orthant in two-dimensional Euclidean space. He/she must choose an allocation in the set, constrained only by Nash's axioms, in the sense that a penalty is paid if and only if a utility allocation is chosen at date T which is inconsistent, according to one of the axioms, with a utility allocation chosen at some earlier date. Penalties are discounted with t, and the Judge chooses any allocation, at a given date, that minimizes the penalty he/she pays at that date. Under what conditions will the Judge's chosen allocations converge to the Nash allocation over time? We answer this question for three canonical axiomatic bargaining solutions: Nash's, Kalai-Smorodinsky's, and the 'egalitarian' solution, and generalize the analysis to a broad class of axiomatic models. |

Tel Aviv University and New York University
(Joint work with Yuval Salant) An individual displays various preference orderings in different payoff-irrelevant circumstances. It is assumed that the variation in the observed preference orderings is the outcome of some cognitive process that distorts the underlying preferences of the individual. We introduce a framework for eliciting the individual's underlying preferences in such cases, and then demonstrate it for two cognitive processes - satisficing and small assessment errors. |

Tel Aviv University and University College London
(Joint work with Michele Piccione) This paper studies market competition when firms can influence consumers' ability to compare market alternatives, through their choice of price "formats". We introduce random graphs as a tool for modeling limited comparability of formats. Our main results concern the interaction between firms' equilibrium price and format decisions and its implications for industry profits and consumer switching rates. In particular, firms earn max-min payoffs in symmetric equilibria if and only if the graph that represents the comparability between formats satisfies a generalized regularity property, which we interpret as a form of "frame neutrality". The same property is necessary for equilibrium behavior to display statistical independence between price and format decisions. We also show that narrow regulatory interventions that aim to facilitate comparisons may have an anti-competitive effect. |

UCL & DIW Berlin
(Joint work with Nadja Dwenger, Dorothea Kübler) We investigate violations of consequentialism in the form of the "stochastic dominance" property. As a basic requirement of many theories of choice, the property implies that lotteries over outcomes are never preferred over receiving the best outcome for sure. We run single-person experiments to demonstrate that the option of dominated randomization can be attractive to many decision-makers. In situations where the decision-maker submits multiple preference lists without knowing which one is relevant, many subjects submit sets of preference lists that contradict each other, thereby inducing a dominated lottery between outcomes. A possible reason for the effect is indecision. A large data set on university applications in Germany shows patterns that are consistent with this effect. |