Doctoral Dissertation Research in Economics: Attention and Beliefs in Games: an Experiment

Columbia University, New York NY

Investigators

Abstract

Abstract: Game theory has become an indispensable tool in the analysis of strategic interactions between people, groups, and nations. It rests on Nash equilibrium as its central concept. In a Nash equilibrium, (1) each player?s action is best, given his or her beliefs over others? actions and (2) those beliefs are correct. However, even under the idealized conditions of laboratory experiments, there are systematic deviations from the predictions of classical game theory. That this is true for even the simplest of games suggests the need to augment the standard theory to predict behavior in more realistic games with policy relevance, such as those used to model firms? decisions to enter markets or countries designing competing trade policies. To reconcile theory with experimental data, this research proposes generalizations of Nash equilibrium that replace conditions (1) and (2) with conditions that allow for players to make mistakes in taking actions and forming beliefs. By collecting experimental data in the laboratory from many simple games, theoretical predictions will be tested and model performance will be assessed. The results will provide a better understanding of how people, organizations, and nations interacting strategically. Better understanding can then translate into better policy-making, more carefully targeted, and more effective in its results. An approach for incorporating mistakes in actions already exists in the literature. Called QRE (quantal response equilibrium), it posits that players make mistakes with probability inversely related to the loss in payoffs the mistakes induce. However, the origins of these mistakes are left unspecified. By relating the mistakes to theories of optimal information processing or ?attention?, the novel EQRE (endogenous QRE) makes different predictions about how these mistakes depend on the game. BBE (biased beliefs equilibrium), on the other hand, suggests a new way of incorporating systematically biased beliefs into an equilibrium framework. A ?bias? is any specific tendency to form mistaken beliefs over the actions of others. Tending to believe one action will be played with greater probability than the equilibrium level and tending to believe that the frequencies of different actions will be more similar than the equilibrium frequencies are two examples of biases. The experiment will involve subjects playing many 2x2 and 3x3 games in which their beliefs are also elicited. Some games are specifically constructed to distinguish between QRE and EQRE. The rest are designed to understand how beliefs, and hence biases, depend on the underlying game. The data set generated by the experiment, together with the theoretical BBE framework, will be suited to answer questions of broader interest, such as: Can biases predict actions in the aggregate? Can actions predict biases in the aggregate? Are individual biases consistent across games and across time? The results have the potential to make a significant contribution to empirical game theory.