We study an evolutionary game involving two populations sharing the same strategies, but with different payoff matrices. Under pairwise imitation, a revising individual can be paired with and imitate agents belonging to the same and also the alternative population. In the second case, his payoff diverges from the observed payoff of his pair. The asymptotically stable equilibrium depends on the confidence agents assign to what they see versus their own estimation. We analyze how the equilibrium differs from Nash and how it is affected by the confidence agents assign to what they see.
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