Imitative Behavior in a Two-Population Model
We study an evolutionary game with two asymmetric populations where agents from each population are randomly paired with members of the other population. We present two imitation models. In the first model, dissatisfaction drives imitation. In the second model, agents imitate the successful. In the first model, we use a simple reviewing rule, while in the second model we use a proportional imitation rule where switching depends on agents comparing their payoffs to others’ payoffs. We show that such imitative behavior can be approximated by a replicator dynamic system. We characterize the evolutionarily stable strategies for a two asymmetric populations normal form game and we show that a mixed strategy is evolutionary stable if and only if it is a strict Nash equilibrium. We offer one clear conclusion: whom an agent imitates is more important than how an agent imitates.
KeywordsNash Equilibrium Equilibrium Point Mixed Strategy Pure Strategy Stable Strategy
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