Learning Equilibria in Games Played by Heterogeneous Populations

Y.M. Kaniovski, A.V. Kryazhimskii and H. Young

Working Papers from International Institute for Applied Systems Analysis

Abstract: Consider two populations of agents who learn to play a game through. repetition. In fictitious play, each agent chooses a best replay to the frequency distribution of actions taken by the other side. A natural variant of this model is to assume that agents are heterogeneous in their information and their behavioral response rules. Assume that each agent knows only a randomly drawn sample of past actions. Given their information, agents sometimes choose best replies, and sometimes they imitate behavior in their own population. In contrast to the stochastic best reply dynamics studied by Fudenberg and Kreps (1993), Kaniovski and Young (1995), and Benaiem and Hirsch (1994), such process can cycle in a 2x2 game even when the probability of imitators is arbitrarily small. We show how to characterize its asymptotic behavior through an extension of Bendixon's theory for excluding cycles combined with standard techniques from stochastic approximation. \f2Journal of Economic Literature\f1 Classification Numbers: C44, C73, D83.

Date: 1997-03
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