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Do boundedly rational players learn to choose equilibrium strategies as theyplay a game repeatedly? A large literature in behavioral game theory hasproposed and experimentally tested various learning algorithms, but acomparative analysis of their equilibrium convergence properties is lacking. Inthis paper we analyze Experience-Weighted Attraction (EWA), which generalizesfictitious play, best-response dynamics, reinforcement learning and alsoreplicator dynamics. Studying $2\times 2$ games for tractability, we recoversome well-known results in the limiting cases in which EWA reduces to thelearning rules that it generalizes, but also obtain new results for otherparameterizations. For example, we show that in coordination games EWA may onlyconverge to the Pareto-efficient equilibrium, never reaching thePareto-inefficient one; that in Prisoner Dilemma games it may converge to fixedpoints of mutual cooperation; and that limit cycles or chaotic dynamics may bemore likely with longer or shorter memory of previous play.

Towards a taxonomy of learning dynamics in 2 x 2 games