A Note on Equilibrium Selection in Polya-Urn Coordination Games

We study equilibrium selection in coordination games played by a population whose size increases over time. In each time period, a new player enters the economy, observes current strategy shares and irreversibly chooses a strategy on the basis of expected payoffs. We employ a simple Polya-Urn scheme to discuss the efficiency of long-run equilibria under alternative individual decision rules (e.g. best-reply, logit, etc.). We show that the system delivers a predictable outcome only when agents employ either a linear or a logit probability rule. If agents employ deterministic best-reply rules, Pareto-efficient coordination can occur, but the actual outcome depends on initial conditions and chance. In all other cases, coexistence of strategies characterizes equilibrium configurations.