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Rational Choice, Decision and Game Theory

Penn is ranked among the top philosophy programs in Rational Choice, Decision and Game theory.

Game theory aims to understand situations in which decision makers interact. Chess is an example, as are firms competing for business, politicians competing for votes, jury members deciding on a verdict, animals fighting over prey, bidders competing in auctions, or threats and punishments in longterm relationships. What all these situations have in common is that the outcome of the interaction depends on what the parties jointly do. Decision makers may be people, organizations, animals, robots or even genes. The theory of rational choice is a basic component of game-theoretic models. This theory has been criticized from a descriptive viewpoint, arguing that it requires way too much calculating capabilities from ordinary beings that use, at most, simple heuristics. Few however have given a close and critical look at how a normative theory of rational choice fares in interactive decision contexts. What does it mean to be rational when the outcome of one's action depends upon the actions of other people and everyone is trying to guess what the others will do? How do separated agents succeed in coordinating their actions so that the formal outcome is the result of each agent's rational choice? In social interaction, rationality has to be enriched with further assumptions about individuals' mutual knowledge and beliefs, but these assumptions are not without consequence.

Cristina Bicchieri has been working on the epistemic foundations of game theory, analyzing the consequences of relaxing the 'common knowledge' assumption in several classes of games. Her contributions include axiomatic models of players' theory of the game and the proof that -- in a large class of games -- a player's theory of the game is consistent only if the player's knowledge is limited. An important consequence of assuming bounded knowledge is that it allows for more intuitive solutions to familiar games such as the finitely repeated prisoner's dilemma or the chain-store paradox. Bicchieri has also been interested in devising mechanical procedures (algorithms) that allow players to compute solutions for games of perfect and imperfect information. Devising such procedures is particularly important for Artificial Intelligence applications, since interacting software agents have to be programmed to play a variety of 'games'.

Learning and belief revision are important elements of what we mean by rationality. Weinstein and Domotor have done seminal work on learning, and Bicchieri has worked on models of belief revision in games.

A challenge to the established theories of rationality comes from experimental economics. Experimental results on Trust, Ultimatum and Social Dilemma games show that people do not behave as predicted by traditional game-theoretic models. This does not mean individuals are irrational, it just means that some auxiliary hypotheses (such as material self-interest) have a much narrower scope. Economists have advanced several models of social preferences to explain the results, but we are still searching for utility functions general enough to subsume many different behaviors and specific enough to allow for meaningful predictions. Bicchieri most recent research focus has been judgment and decision making with special interest in decisions about fairness, trust, and cooperation, and how expectations affect behavior. Her theory of social norms provides an alternative utility function that takes into account the fact that most individuals have a conditional preference for following a social norm, provided certain empirical and normative expectations are met. Her experiments test whether manipulating expectations changes behavior (it does), the relative importance of normative vs. empirical expectations, especially when they are in conflict (empirical expectations win), and how to detect whether a norm is actually in place.

Faculty and students can use a lab where to conduct experiments, and Penn has a large Behavioral Decision Making interdisciplinary group.