The Evolution of Beliefs in a Finitely Repeated Game

Abstract

"Consider an agent playing a series of games against opponents drawn from a given population composed of various player types. The choice of a strategy then depends critically on the agent's beliefs about the distribution of types present in the population. Beliefs evolve with playing experience, and if play converges to an equilibrium, so do beliefs. In this paper we model evolution according to the replicator dynamics drawn from evolutionary stability theory. We examine a finitely repeated coordination game played against two types of randomly drawn opponents, human and robot. By controlling the distribution of types and initial beliefs, we achieve experimental control over the evolution of beliefs. Our major result is that in a wide variety of designs and treatments human subject play does converge to an evolutionarily stable strategy."