Minimal belief revision leads to backward induction

We present an epistemic model for games with perfect information in which players, upon observing an unexpected move, may revise their belief about the opponents’ preferences over outcomes. For a given profile pp of preference relations over outcomes, we impose the following conditions: (1) players initially believe that opponents have preference relations as specified by pp; (2) players believe at every instance of the game that each opponent is carrying out a sequentially rational strategy; (3) if a player revises his belief about an opponent’s type, he must search for a “new” type that disagrees with the “old” type on a minimal number of statements about this opponent; (4) if a player revises his belief about an opponent’s preference relation over outcomes, he must search for a “new” preference relation that disagrees with the “old” preference relation on a minimal number of pairwise rankings. It is shown that every player whose preference relation is given by pp, and who throughout the game respects common belief in the events (1)–(4), has a unique sequentially rational strategy, namely his backward induction strategy in the game induced by pp.