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We consider a model of cultural evolution for a strategy selection in apopulation of individuals who interact in a game theoretic framework. Theevolution combines individual learning of the environment (population strategyprofile), reproduction, proportional to the success of the acquired knowledge,and social transmission of the knowledge to the next generation. A mean-fieldtype equation is derived that describes the dynamics of the distribution ofcultural traits, in terms of the rate of learning, the reproduction rate andpopulation size. We establish global well-posedness of the initial-boundaryvalue problem for this equation and give several examples that illustrate theprocess of the cultural evolution for some classical games.

A model of cultural evolution in the context of strategic conflict