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Graphexon Mean Field Games on Large Network Limits

Peter E. Caines, Minyi Huang · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27292 · cited by 0 works (OpenAlex) · open-access PDF

Portuguese

Este artigo analisa os jogos de campo médio de grafexon (GXMFG) em grandes limites de rede. Ao considerar distribuições de borda de uma sequência de gráficos finitos, definimos as medidas de grafexon empíricas e estudamos seus limites fracos subsequentes em um espaço de grafexon consistindo de todas as medidas de probabilidade simétricas em $[0,1]^{2d}$. Este conceito de limites de rede estende a teoria de grafon para redes gerais, não necessariamente densas. Para formular o jogo usando o limite de grafexon, exploramos uma propriedade útil de que uma medida de probabilidade em um espaço de produto é o produto de um núcleo de probabilidade e uma distribuição marginal. Com base em tais limites de gráficos e o núcleo de probabilidade da medida de grafexon associ

Machine translation (Meta M2M100); the English original follows.

Abstract

This paper analyzes graphexon mean field games (GXMFG) on large network limits. By considering edge distributions of a sequence of finite graphs, we define the empirical graphexon measures and study their subsequential weak limits in a graphexon space consisting of all symmetric probability measures on $[0,1]^{2d}$. This concept of network limits extends graphon theory to general, not necessarily dense, networks. To formulate the game using the graphexon limit, we exploit a useful property that a probability measure on a product space is the product of a probability kernel and a marginal distribution. Based on such graph limits and the probability kernel of the associated graphexon measure, we derive the GXMFG equations, and present a detailed analysis for the linear-quadratic case. For linear-quadratic models with finite populations residing over large networks, we use the GXMFG equations to construct decentralized strategies, for which an $ε$-Nash equilibrium property is established.

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Topics: Probability measure, Mathematics, Property (philosophy), Product topology, Measure (data warehouse), Kernel (algebra)

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