Social coordination with locally observable types

In this paper we study the typical dilemma of social coordination between a risk-dominant convention and a payoff-dominant convention. In particular, we consider a model where a population of agents play a coordination game over time, choosing both the action and the network of agents with whom to interact. The main modeling novelties with respect to the existing literature are: (1) Agents come in two distinct types, (2) the interaction with a different type is costly, and (3) an agent’s type is unobservable prior to interaction. We show that when the cost of interacting with a different type is small with respect to the payoff of coordination, the payoff-dominant convention is the only stochastically stable convention; instead, when the cost of interacting with a different type is large, the only stochastically stable conventions are those where all agents of one type play the payoff dominant action and all agents of the other type play the risk-dominant action.