RATIONALITY ON FINAL DECISIONS LEADS TO SEQUENTIAL EQUILIBRIUM∗

The purpose of this article is to investigate epistemic conditions for a sequential equilib-rium in an extensive form game with imperfect information: If players mutually know that all players maximize their own expected payoffs at any information sets in their final decisions then their behaviors with belief yield a sequential equilibrium. This result is an extension of Aumann (1995, Games and Economic Behavior, 8:6-19) in a perfect infor-mation game. In this article, we propose the notion of µ-rationality, by which we mean that player knows that he maximizes his own payoff according to the common-belief µ. Furthermore we introduce the notion of µ-consistency in imperfect information game. Our main theorem states that mutual knowledge of both µ-rationality and µ-consistency induces a sequential equilibrium outcome in an extensive form game