Adaptation and complexity in repeated games

A learning model is constructed for two-player repeated games. In an inference step players construct minimally complex models of strategies based on observed play, and in an adaptation step players choose minimally complex best responses to an inference. When both players have optimistic inferences, stage game Nash equilibria are played in all steady states in the set of finite state automata, while under cautious inferences the set of steady states is the subset of self-confirming equilibria with Nash outcome paths. Convergence to these steady states is demonstrated in the Prisoner’s Dilemma when the initial conditions have at most two states. Journal of Economic Literature Classification Numbers: C72, D83.