Strategic behavior and counterfactuals

The difficulty of defining rational behavior in game situations is that the players' strategies will depend on their expectations about other players' strategies. These expectations are beliefs the players come to the game with. Game theorists assume these beliefs to be rational in the very special sense of beingobjectively correct but no explanation is offered of the mechanism generating this property of the belief system. In many interesting cases, however, such a rationality requirement is not enough to guarantee that an equilibrium will be attained. In particular, I analyze the case of multiple equilibria, since in this case there exists a whole set of rational beliefs, so that no player can ever be certain that the others believe he has certain beliefs. In this case it becomes necessary to explicitly model the process of belief formation. This model attributes to the players a theory of counterfactuals which they use in restricting the set of possible equilibria. If it were possible to attribute to the players the same theory of counterfactuals, then the players' beliefs would eventually converge.I wish to thank Michael Bacharach, In-Koo Cho, William Harper, Aanund Hylland, Isaac Levi, Wolfgang Spohn, Tommy Tan and two anonymous referees for many useful comments and suggestions. Financial support from National Science Foundation grant SES 87-10209 is gratefully acknowledged.