Reasoning about Your Own Future Mistakes

We propose a model of reasoning in dynamic games in which a player, at each information set, holds a conditional belief about his own future choices and the opponents' future choices. These conditional beliefs are assumed to be cautious, that is, the player never completely rules out any feasible future choice by himself or the opponents. We impose the following key conditions: (a) a player always believes that he will choose rationally in the future, (b) a player always believes that his opponents will choose rationally in the future, and (c) a player deems his own mistakes infinitely less likely than the opponents' mistakes. These conditions, together with iterating property (b), lead to the new concept of perfect backwards rationalizability. We show that perfect backwards rationalizable strategies exist in every finite dynamic game. We prove, moreover, that perfect backwards rationalizability constitutes a refinement of both perfect rationalizability (a rationalizability analogue to Selten's (1975) perfect equilibrium) and procedural quasi-perfect rationalizability (a rationalizability analogue to van Damme's (1984) quasi-perfect equilibrium) – two concepts that are introduced in this paper. As a consequence, our concept avoids both weakly dominated strategies in the normal form and strategies containing weakly dominated actions in the agent normal form. For one-shot games, the concept coincides with permissibility (Brandenburger (1992), Börgers (1994)).