Rationalizability and minimal complexity in dynamic games

This paper presents a formal epistemic framework for dynamic games in which players, during the course of the game, may revise their beliefs about the opponents' utility functions. We impose two key conditions upon the players' beliefs: (a) throughout the game, every move by the opponent should be interpreted as a rational move, and (b) the belief about the opponents' relative utilities between two terminal nodes should only be revised if you are sure that the opponent has decided to avoid one of these nodes. Common belief about these events leads to the concept of persistent rationalizability. It is shown that persistent rationalizability implies the backward induction procedure in generic games with perfect information. We next focus on persistently rationalizable types having beliefs with "minimal complexity", resulting in the concept of minimal rationalizability. For two-player simultaneous move games, minimal rationalizability is equivalent to the concept of Nash equilibrium strategy. In every outside option game, as defined by van Damme (1989), minimal rationalizability uniquely selects the forward induction outcome.