  Do boundedly rational players learn to choose equilibrium strategies as they
play a game repeatedly? A large literature in behavioral game theory has
proposed and experimentally tested various learning algorithms, but a
comparative analysis of their equilibrium convergence properties is lacking. In
this paper we analyze Experience-Weighted Attraction (EWA), which generalizes
fictitious play, best-response dynamics, reinforcement learning and also
replicator dynamics. Studying $2\times 2$ games for tractability, we recover
some well-known results in the limiting cases in which EWA reduces to the
learning rules that it generalizes, but also obtain new results for other
parameterizations. For example, we show that in coordination games EWA may only
converge to the Pareto-efficient equilibrium, never reaching the
Pareto-inefficient one; that in Prisoner Dilemma games it may converge to fixed
points of mutual cooperation; and that limit cycles or chaotic dynamics may be
more likely with longer or shorter memory of previous play.
