A behavioral learning process in games

This paper studies the cumulative proportional reinforcement (CPR) rule, ac cording to which an agent plays, at each period, an action with a probabili ty proportional to the cumulative utility that the agent has obtained with that action. The asymptotic properties of this learning process are examine d for a decision-maker under risk, where it converges almost surely toward the expected utility maximizing action(s). The process is further considere d in a two-player game; it converges with positive probability toward any s trict pure Nash equilibrium and converges with zero probability toward some mixed equilibria (which are characterized). The CPR rule is compared in it s principles with other reinforcement rules and with replicator dynamics. ( C) 2001 Academic Press.