Dynamic Equilibrium Selection: A General Uniqueness Result

This paper shows that in a dynamic context, under weak assumptions, the presence of payoff shocks can shrink the equilibrium set to a singleton. We study a model with a continuum of fully rational agents who switch between two actions or states over time (e.g., working in different sectors, employment vs. unemployment, etc.). An agent's incentive to pick a given action is greater if others do the same. Agents receive chances to change actions at random times and may influence the rate at which these chances arrive. Payoff shocks may follow any of a large class of stochastic processes that includes both seasonal and mean-reverting processes. In this general setting, payoff shocks give rise to a unique equilibrium. One implication is that the introduction of aggregate shocks leads to a unique equilibrium in two well-known macroeconomic search models with multiple equilibria (Diamond and Fudenberg, Howitt and McAfee).