Identifying Strategies and Beliefs Without Rationality Assumptions

Abstract

In this paper we formulate a solution concept without making assumptions about expected utility maximization, common knowledge or beliefs. Beliefs, strategies and the degree to which players are expected utility maximizers are endogenously determined as part of the solution. To achieve this, rather than solving the game from the players' point of view, we analyze the game as an "observer" who is not engaged in the process of the game. Our approach is an information theoretic one in which the observer utilizes an observation of play and the Maximum Entropy principle. We compare our solution concept with Bayesian Nash equilibrium and offer the entropy ratio test as a method for determining the appropriateness of common modeling assumptions. We also demonstrate that the QRE concept can be significantly generalized when viewed from the observer's perspective. For games of incomplete information we discover that alternative uses of the observer's information lead to alternative interpretations of rationality. These alternative interpretations of rationality may prove useful, especially in the context of ex post arbitration, as they indicate who is motivating whom.

Keywords: incomplete information, entropy, information theory, pairwise rationality, QRE, endogenous rationality

JEL Classification: C70, C79