The Dynamics of Norms and Conventions under Local Interactions and Imitation

Restricting the analysis to general 2×2 coordination games, this article shows how under certain conditions, it is highly likely that individuals coordinate on a (pay-off) efficient through risk inferior convention. This contrasts with other equilibrium refinement criteria, such as risk dominance or stochastic stability. Here it is assumed that players are situated on a toroidal regular lattice, interact only locally and, in each period, imitate the last period's most successful player in their neighborhood. If the set of observable players by an individual and the set that he interacts with are both identical and small, pay-off dominance plays the major role in defining the long-term convention. As the latter set of players increases, a risk dominant but pay-off inferior convention becomes more likely. The model also shows that the interaction of two player types in a nonsymmetric game potentially leads to nonegalitarian conventions.