Minimal belief revision leads to backward induction

In this paper we present a model for games with perfect information in which the players, upon observing an unexpected move, may revise their beliefs about the opponents’ preferences over outcomes. For a given profile P of preference relations over outcomes, we impose the following three principles: (1) players initially believe that opponents have preference relations as specified by P ; (2) players believe at every instance of the game that each opponent is carrying out an optimal strategy; and (3) beliefs about the opponents’ preference relations over outcomes should be revised in a minimal way. It is shown that every player whose preference relation is given by P, and who throughout the game respects common belief in the events (1), (2) and (3), has a unique optimal strategy, namely his backward induction strategy in the game induced by P.We finally show that replacing the minimal belief revision principle (3) by the more modest requirement of Bayesian updating leads exactly to the Dekel-Fudenberg procedure in the game induced by P.