Heterogeneity and aggregation in evolutionary dynamics: a general framework without aggregability
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We consider general evolutionary dynamics under persistent payoff heterogeneity and study the dynamic relation between the strategy composition over different types and the aggregate strategy distribution of the entire population. It is rigorously proven that continuity of either the revision protocol or the type distribution guarantees the existence of a unique solution trajectory. In many major evolutionary dynamics, an agent's switching rate between actions increases with the payoff gain from this switch, which causes nonaggregability: the current strategy composition must be identified to predict the transition of the aggregate strategy. Looking at the strategy composition, we retain equilibrium stationarity in general and stability in potential games under admissible dynamics. Local stability of an equilibrium composition under any admissible dynamic can be tested by local stability of the corresponding aggregate equilibrium under the best response dynamic with i.i.d. payoff perturbation. All the results are maintained under heterogeneity in revision protocols.
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