Competing Conventions with Costly Information Acquisition

We consider an evolutionary model of social coordination in a 2x2 game where two groups of players prefer to coordinate on different actions. Players can pay a cost to learn their opponent's group: if they pay it, they can condition their actions on the groups. 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, players never learn the group 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 player plays that group's favorite action. If both groups are strong enough in preferences, or if none of the group's size is large enough, players play their favorite actions and miscoordinate in inter-group interactions. Lower levels of the cost favor coordination. Indeed, when the cost is low, in inside-group interactions, players always coordinate on their favorite action, while in inter-group interactions, they coordinate on the favorite action of the group that is stronger in preferences or large enough.