Repeated Coordination with Private Learning

TL;DR

This paper analyzes a repeated coordination game with private signals and externalities, demonstrating the existence of stable equilibria where players learn to coordinate on the true state and achieve efficiency at high discount factors.

Contribution

It introduces the existence of stable equilibria in repeated games with private learning, showing coordination and efficiency are achievable despite initial uncertainties.

Findings

Stable equilibria exist where players learn to coordinate on the true state.

Players can achieve efficient payoffs at high discount factors.

Coordination is possible even with unfavorable signal realizations.

Abstract

We study a repeated game with payoff externalities and observable actions where two players receive information over time about an underlying payoff-relevant state, and strategically coordinate their actions. Players learn about the true state from private signals, as well as the actions of others. They commonly learn the true state (Cripps et al., 2008), but do not coordinate in every equilibrium. We show that there exist stable equilibria in which players can overcome unfavorable signal realizations and eventually coordinate on the correct action, for any discount factor. For high discount factors, we show that in addition players can also achieve efficient payoffs.