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Differential Equation Approximations for Population Games using Elementary Probability

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arxiv 2312.07598 v1 pith:TQVPJTEJ submitted 2023-12-11 cs.GT cs.MAcs.SYeess.SYmath.DSmath.PRstat.AP

Semih Kara , Nuno C. Martins This is my paper · ORCID
classification cs.GTcs.MAcs.SYeess.SYmath.DSmath.PRstat.AP
keywords agentsdifferentialgamespopulationprobabilitystrategicaccessibleadvanced
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Population games model the evolution of strategic interactions among a large number of uniform agents. Due to the agents' uniformity and quantity, their aggregate strategic choices can be approximated by the solutions of a class of ordinary differential equations. This mean-field approach has found to be an effective tool of analysis. However its current proofs rely on advanced mathematical techniques, making them less accessible. In this article, we present a simpler derivation, using only undergraduate-level probability.

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Cited by 1 Pith paper

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  1. Aggregate Fictitious Play for Learning in Anonymous Polymatrix Games (Extended Version)

    cs.GT 2025-08 conditional novelty 6.0 of 10

    In anonymous polymatrix games, fictitious play can be run on aggregate action counts without changing agents' best responses or losing convergence to Nash equilibrium.

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