Competing Conventions with Costly Acquisition of Information

We consider an evolutionary model of social coordination in a 2x2 game where two groups of agents prefer to coordinate on different actions. Agents can pay a cost to learn their opponent's type: conditional on this decision, they can play different actions with different types. We assess the stability of outcomes in the long-run using stochastic stability analysis. We find that three elements matter for the equilibrium selection: the group size, the strength of preferences, and the information's cost. If the cost is too high, agents never learn the type of their opponents in the long-run. If one group is stronger in preferences for its favorite action than the other, or its size is sufficiently large compared to the other group, every agent plays that action. If both groups are strong enough in preferences, or if none of the group's size is large enough, agents play their favorite actions and miscoordinate in inter-group interactions. When the cost is sufficiently low, agents always coordinate. In inside-group interactions, agents always coordinate on their favorite action. In inter-group interactions, they coordinate on the favorite action of the group that is stronger in preferences or large enough.