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arXiv · 2505.13632

Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games

Hui Huang·Jethro Warnett
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Abstract

Recently, the paper [12] introduces a derivative-free consensus-based particle method that finds the Nash equilibrium of non-convex multiplayer games, where it proves the global exponential convergence in the sense of mean-field law. This paper aims to address theoretical gaps in [12], specifically by providing a quantitative estimate of the mean-field limit with respect to the number of particles, as well as establishing the well-posedness of both the finite particle model and the corresponding mean-field dynamics.

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Hui Huang, Jethro Warnett. 2025-05-19. Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games. https://arxiv.org/abs/2505.13632

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