Belief in the opponents' future rationality

For dynamic games we consider the idea that a player, at every stage of the game, believes that his opponents will choose rationally in the future. Not only this, we also assume that players, throughout the game, believe that their opponents always believe that their opponents will choose rationally in the future, and so on. This leads to the concept of common belief in future rationality, which we formalize within an epistemic model. Our main contribution is to present an iterative elimination procedure, backward dominance, that selects exactly those strategies that can rationally be chosen under common belief in future rationality. The algorithm proceeds by successively eliminating strategies at every information set of the game. More speci…cally, in round k of the procedure we eliminate at a given information set h those strategies for player i that are strictly dominated at some player i information set h0 weakly following h, given the opponents’ strategies that have survived at h0 until round k. Key words and phrases: Epistemic game theory, dynamic games, belief in future rationality, backward dominance procedure, backward induction. Journal of Economic Literature Classi…cation: C72 Contact information: Maastricht University, Department of Quantitative Economics P.O. Box 616, 6200 MD Maastricht, The Netherlands [email protected] Webpage: http://www.personeel.unimaas.nl/a.perea/ I would like to thank Christian Bach, Pierpaolo Battigalli, Aviad Heifetz and some anonymous referees for useful comments and suggestions.