Coherent Belief Revision And Equilibrium Selection In Games

What predictions about behavior in extensive form games can we rigorously justify as implied by rationality or mutual or common knowledge of that rationality? This paper models rational belief revision in extensive form games and uses numerical methods to examine the implications for equilibrium predictions. In general, in dynamic strategic choice situations, the method of belief revision adopted by the players will determine which of a set of possible equilibria (or non-Nash strategy choices) is selected. This intuition has motivated critiques of subgame perfection, including the argument that the reasoning supporting backward induction is paradoxical. This paper examines this question with models of the dynamics of transitions between epistemic states. These models give belief revision functions which are well-defined for updating on zero probability events and are equivalent to Bayesian updating where that is defined. Thus the gap between the standard game model and the intuition driving some of the critiques of backward induction can be bridged with this approach. It appears that the class of equilibria that we obtain with this model are neither implied by, nor imply, Nash equilibrium. The sequential nature of the definition of individual rationality and the possibility of rational belief revision yield a model which implies sequential equilibrium when there is sufficient mutual knowledge of rationality and selects equilibria that satisfy forward induction. But since neither knowledge of the other players' sequential rationality nor correct beliefs are imposed, non-Nash, but individually sequentially rational, outcomes are also supported in equilibrium.