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Asymmetric Replicator Dynamics on Polish Spaces: Invariance, Stability, and Convergence

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  • Karl D. Lewis

    (Indian Institute of Technology Madras)

  • A. J. Shaiju

    (Indian Institute of Technology Madras)

Abstract

We study a class of asymmetric games with compact Polish strategy sets and provide sufficient conditions for the stability and convergence of profiles under the infinite-dimensional replicator dynamics on such games. We apply these results to analyze the dynamic behavior of the Cournot duopoly with different pricing mechanisms, the rope-pulling game, and a game with a Nash equilibrium profile consisting of uniform distributions. Further, we prove that the set of all Gaussian profiles remains invariant under the replicator dynamics on a large class of quadratic games. Moreover, we study the dynamics restricted to the set of Gaussian profiles, both analytically and numerically.

Suggested Citation

  • Karl D. Lewis & A. J. Shaiju, 2024. "Asymmetric Replicator Dynamics on Polish Spaces: Invariance, Stability, and Convergence," Dynamic Games and Applications, Springer, vol. 14(5), pages 1160-1190, November.
    • Handle: RePEc:spr:dyngam:v:14:y:2024:i:5:d:10.1007_s13235-023-00546-3
    DOI: 10.1007/s13235-023-00546-3
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    References listed on IDEAS

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