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

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  • Dai Zusai

    (Tohoku University
    Temple University)

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 existing literature, we do not assume anonymity of the game nor aggregability of the dynamic. The dynamic is formulated as a differential equation of a joint probability measure of types and strategies. To establish a foundation for 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 encompasses a wide range of possible applications, including incomplete information games and spatial evolution.

Suggested Citation

  • Dai Zusai, 2023. "Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(4), pages 1215-1260, December.
    • Handle: RePEc:spr:jogath:v:52:y:2023:i:4:d:10.1007_s00182-023-00867-y
    DOI: 10.1007/s00182-023-00867-y
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    Keywords

    Evolutionary dynamics; Heterogeneity; Continuous space; Potential games;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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