Common reasoning in games: a Lewisian analysis of common knowledge of rationality*

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 are grateful for comments on earlier versions of the paper to Giacomo Bonnano, Adam Brandenburger, John Collins and participants in various seminars, conferences and workshops at which we have presented the paper. Abstract The game-theoretic assumption of 'common knowledge of rationality' leads to paradoxes when rationality is represented in a Bayesian framework as cautious expected utility maximisation with independent beliefs (ICEU). We diagnose and resolve these paradoxes by presenting a new class of formal models of players' reasoning, inspired by David Lewis's account of common knowledge, in which the analogue of common knowledge is derivability in common reason. We show that such models can consistently incorporate any of a wide range of standards of decision-theoretic practical rationality. We investigate the implications arising when the standard of decision-theoretic rationality so assumed is ICEU.