Interaction and imitation with heterogeneous agents: A misleading evolutionary equilibrium

Abstract

In a two-population evolutionary game we analyze the interaction between individuals belonging to two populations with the same strategy set but different payoffs. Agents play a game against individuals in the two populations. They imitate agents belonging to the same and also the alternative population. When a revising agent is matched with an individual in the alternative population who plays differently, his expected payoff and the observed payoff of his partner diverge. Hence, he conjectures the payoff from switching to the other strategy by weighing what he expected and what he observes. The evolutionary dynamics has a unique asymptotically stable fixed point, which typically differs from the evolutionary stable equilibrium without inter-population imitation. For a collective action game we analyze to what extent the compliance rate and the social welfare differ from the Nash equilibrium, and how these gaps depend on the confidence that agents assign to what they see.