A Note on Equilibrium Selection in Polya−Urn Coordination

We study equilibrium selection in coordination games played by a population of agents whose size increases over time. We assume that, 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. Finally, we discuss our findings in the framework of technological adoption models