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

Karl D. Lewis () and A. J. Shaiju ()
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Karl D. Lewis: Indian Institute of Technology Madras
A. J. Shaiju: Indian Institute of Technology Madras

Dynamic Games and Applications, 2024, vol. 14, issue 5, No 4, 1160-1190

Abstract: 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.

Keywords: Evolutionary game theory; Replicator dynamics; Asymmetric games with continuous strategy sets; Evolutionary stability; Dynamic stability; 91A22; 91A26; 92D25; 34D20; 34D45; 34G20 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13235-023-00546-3

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