Interaction and imitation with heterogeneous agents: A misleading evolutionary equilibrium

Abstract

• A two-population evolutionary game involving selfish and pro-social agents. • Heterogeneous individuals interact and also imitate one another. • Uncertainty leads a revising agent to misleadingly imitate other population agents. • Inter-population imitation gives rise to a unique asymptotically stable fixed point. • In this misleading equilibrium selfish and pro-social behavior diverge from the NE. In a two-population evolutionary game we analyze the interaction between individuals belonging to two populations with the same strategy set but different payoffs. A game is played among individuals in the two populations. They imitate agents belonging to the same and also the alternative population. When a revising agent is matched with someone 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 locally 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.