Limited Backward Induction as an Expression of Bayesian Rationality

The paper explores the consequences of assuming that players involved in a complex perfect-information game perceive the situation as one of incomplete information, in the sense that, at any given decision node, players are certain about the structure of the game tree only within a limited horizon. Our main result says that there are valuations of the nodes at the end of the players' horizons such that sequential equilibrium behavior in the incomplete-information game reflects 'limited' backward induction reasoning in the true game. We also show that a longer horizon is beneficial for a player in strictly competitive games, but not in general.