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.
