Belief in the opponentsʼ future rationality

•We present the concept of common belief in future rationality for general dynamic games.•We present an algorithm that yields precisely those strategies you can rationally choose under common belief in future rationality.•We compare the concept and algorithm to other related concepts and algorithms in the literature.

For dynamic games we consider the idea that a player, at every stage of the game, will always believe that his opponents will choose rationally in the future. This is the basis for the concept of common belief in future rationality, which we formalize within an epistemic model. We present an iterative procedure, backward dominance, that proceeds by eliminating strategies from the game, based on strict dominance arguments. We show that the backward dominance procedure selects precisely those strategies that can rationally be chosen under common belief in future rationality if we would not impose (common belief in) Bayesian updating.