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A general framework of evolutionary dynamics under heterogeneous populationsis presented. The framework allows continuously many types of heterogeneousagents, heterogeneity both in payoff functions and in revision protocols andthe entire joint distribution of strategies and types to influence the payoffsof agents. We clarify regularity conditions for the unique existence of asolution trajectory and for the existence of equilibrium. We confirm thatequilibrium stationarity in general and equilibrium stability in potentialgames are extended from the homogeneous setting to the heterogeneous setting.In particular, a wide class of admissible dynamics share the same set oflocally stable equilibria in a potential game through local maximization of thepotential.

Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution