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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

Spanish

Este artículo analiza los juegos de campo medio de grafeno (GXMFG) en grandes límites de red. Al considerar las distribuciones de borde de una secuencia de gráficos finitos, definimos las medidas de grafeno empíricas y estudiamos sus límites débiles subsecuentes en un espacio de grafeno que consiste en todas las medidas de probabilidad simétricas en $[0,1]^{2d}$. Este concepto de límites de red extiende la teoría de grafeno a redes generales, no necesariamente densas. Para formular el juego utilizando el límite de grafeno, aprovechamos una propiedad útil de que una medida de probabilidad en un espacio de producto es el producto de un núcleo de probabilidad y una distribución marginal. Basado en tales límites y el núcleo de probabilidad de la medida de grafeno asociada, derivamos las ecua

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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