Associate Professor, Graduate School of Economics and Management, Tohoku University

We present a general framework of evolutionary dynamics under persistent heterogeneity in payoff functions and revision protocols, allowing continuously many types in a game with finitely many strategies. Unlike the preceding literature, we do not assume anonymity of the game or aggregability of the dynamic. The dynamic is rigorously formulated as a differential equation of a joint probability measure of types and strategies. To establish a foundation of this framework, we clarify regularity assumptions on the revision protocol, the game and the type distribution to guarantee the existence of a unique solution trajectory as well as those to guarantee the existence of an equilibrium in a heterogeneous population game. We further verify equilibrium stationarity in general and stability in potential games under admissible dynamics. Our framework exhibits a wide range of possible applications, including equilibrium selection in Bayesian games and spatial evolution.