Adaptive Play by Idiosyncratic Agents

Equilibrium selection in coordination games has generated a large literature. Kandori, Mailath and Rob [Econometrica 61 (1993) 29] and Young [Econometrica 61 (1993) 57] studied dynamic models of aggregate behaviour where agents best-respond to observations of population play. Crucially, infrequent mistakes ("mutations") allow agents to take actions contrary to current trends and prevent initial configurations from determining long-run play. An alternative approach is offered here: Trembles are added to payoffs so that with some probability it is optimal to act against the flow of play. The long-run distribution of population behaviour is characterised--modes correspond to stable Bayesian Nash equilibria. Allowing the variance of payoff trembles to vanish (a purification process) a single equilibrium is played almost always in the long run. Kandori, Mailath, and Rob, and Young, show that the number of contrary actions required to escape an equilibrium determines selection; here, the likelihood that such actions are taken is equally important.