Multipopulation replicator dynamics with erroneous perceptions

In evolutionary game theory, to the best of our knowledge, individuals´ perceptions have been disregarded. When an individual interacts with the other individual under coexistence of heterogeneous sub-populations, it is natural that the individual changes its strategy depending on the sub-population the other individual belongs to. Moreover, in such a situation, each individual may make an error about the sub-population the other individual belongs to. We propose a multipopulation model with erroneous perceptions. We define an evolutionary stable strategy (ESS) and formulate replicator dynamics in this model, and prove several properties of the proposed model.