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

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  • Dai Zusai

Abstract

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.

Suggested Citation

  • Dai Zusai, 2021. "Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution," TUPD Discussion Papers 2, Graduate School of Economics and Management, Tohoku University.
    • Handle: RePEc:toh:tupdaa:2
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    File URL: http://hdl.handle.net/10097/00131573
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    Cited by:

    1. Sawa, Ryoji & Wu, Jiabin, 2023. "Statistical inference in evolutionary dynamics," Games and Economic Behavior, Elsevier, vol. 137(C), pages 294-316.

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