Common Reasoning in Games

The focus for the Centre is research into individual and strategic decision-making using a combination of theoretical and experimental methods. On the theory side, members of the Centre investigate individual choice under uncertainty, cooperative and non-cooperative game theory, as well as theories of psychology, bounded rationality and evolutionary game theory. Members of the Centre have applied experimental methods in the fields of Public Economics, Individual Choice under Risk and Uncertainty, Strategic Interaction, and the performance of auctions, markets and other economic institutions. Much of the Centre's research involves collaborative projects with researchers from other departments in the UK and overseas. * We dedicate this paper to the late Michael Bacharach, as an acknowledgement of his role in pioneering the analysis of players' reasoning in game theory and in inspiring our interest in exploring the foundations of the theory. We are grateful for comments on earlier versions to a referee and an associate editor; to and to participants in various seminars, conferences and workshops at which we have presented the paper. Abstract This paper makes three related contributions to noncooperative game theory: (i) a solution concept (the " ICEU solution "), which is generated by an iterative procedure that constructs trinary partitions of strategy sets and deals with problems arising from weak dominance; (ii) a class of models of players' reasoning, inspired by David Lewis's work on common knowledge, which can together represent common knowledge of rationality for any consistent conception of individual practical rationality; and, using these ingredients, (iii) a diagnosis of paradoxes associated with the concept of common knowledge of rationality, as represented in Bayesian models of games. Common reasoning in games JEL classification C72 3 1. Introduction This paper makes three main contributions to noncooperative game theory: a solution concept which deals in a new way with the problems arising from weak dominance; a class of models of players' reasoning; and a diagnosis of paradoxes associated with the concept of common knowledge of rationality, as represented in Bayesian models of games. Although seemingly of different types, these contributions are closely related. Our solution concept (the " ICEU solution ") is distinctive in being the output of an iterative procedure which constructs trinary partitions of the set of strategies for the relevant game. At each stage of the procedure, strategies are categorised into those that have been found to be rationally playable, those that have been found to be …