Fast Equilibrium Selection by Rational Players Living in a Changing World

We study a coordination game with randomly changing payoos and small frictions in changing actions. Using only backwards induction, we nd that players must coordinate on the risk dominant equilibrium. More precisely, a continuum of fully rational players are randomly matched to play a symmetric 2 2 game. The payoo matrix changes over time according to some Brownian motion. Players observe these payoos and the population distribution of actions as they evolve. The game has frictions: opportunities to change strategies arrive from independent random processes, so that the players are locked into their actions for some time. We solve the game using only backwards induction. As the frictions disappear, each player ignores what the others are doing and switches at her rst opportunity to the risk dominant equilibrium. History dependence emerges in some cases when frictions remain positive. As an application we show how frictions and aggregate cost shocks can lead to the selection of a unique (and often ineecient) outcome in macroeconomic models that otherwise would have multiple rational expectations equilibria (e.g., Diamond 1991).