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

2025/05/19 by Hui Huang, Huang, Hui, Jethro Warnett +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Distributed Control Multi-Agent Systems #FOS: Mathematics #Mathematical Biology Tumor Growth #Opinion Dynamics and Social Influence #Optimization and Control (math.OC) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2505.13632

openalex publication_date 2025/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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Cited by

• An alternative approach to well-posedness of McKean-Vlasov equations arising in Consensus-Based Optimization

Related

• A consensus-based algorithm for non-convex multiplayer games
• Mean-field limits for Consensus-Based Optimization and Sampling
• Learning Correlated Equilibria in Mean-Field Games
• Nash Equilibrium Approximation under Communication and Computation\n Constraints in Large-Scale Non-cooperative Games
• Linear Quadratic Mean-Field Games with Communication Constraints