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Generalized replicator dynamics based on mean-field pairwise comparison dynamic

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  • Yoshioka, Hidekazu

Abstract

The pairwise comparison dynamic is a forward ordinary differential equation in a Banach space whose solution is a time-dependent probability measure to maximize utility based on a nonlinear and nonlocal protocol. It contains a wide class of evolutionary game models, such as replicator dynamics and its generalization. We present an inverse control approach to obtain a replicator-type pairwise comparison dynamic from the large discount limit of a mean field game (MFG) as a coupled forward-backward system. This methodology provides a new interpretation of replicator-type dynamics as a myopic perception limit of the dynamic programming. The cost function in the MFG is explicitly obtained to derive the generalized replicator dynamics. We present a finite difference method to compute these models such that the conservation and nonnegativity of the probability density and bounds of the value function can be numerically satisfied. We conduct a computational convergence study of a large discount limit, focusing on potential games and an energy management problem under several conditions.

Suggested Citation

  • Yoshioka, Hidekazu, 2025. "Generalized replicator dynamics based on mean-field pairwise comparison dynamic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 236(C), pages 200-220.
    • Handle: RePEc:eee:matcom:v:236:y:2025:i:c:p:200-220
    DOI: 10.1016/j.matcom.2025.04.010
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