Rationality on Final Decisions Leads to Sequential Equilibrium

The purpose of this article is to investigate epistemic conditions for a sequential equilibrium 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 information game. In this article, we propose the nation of 'mu'-rationality, by which we mean that player knows that he maximizes his own payoff according to the common-belief 'mu'. Our main theorem states that mutual knowledge of both 'mu'-rationality and 'mu'-consistency induces a sequential equilibrium outcome in an extensive form game.