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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

German

Dieses Papier analysiert Graphexon Medium Field Games (GXMFG) auf großen Netzwerkgrenzen. Indem wir die Randverteilung einer Sequenz von Endgrafen betrachten, definieren wir die empirischen Graphexon-Maßnahmen und studieren ihre nachfolgenden schwachen Grenzen in einem Graphexon-Raum, der aus allen symmetrischen Wahrscheinlichkeitsmaßnahmen auf $[0,1]^{2d}$ besteht. Dieses Konzept von Netzwerkgrenzen erweitert die Graphon-Theorie auf allgemeine, nicht notwendigerweise dichte Netzwerke. Um das Spiel mithilfe der Graphexon-Limit zu formulieren, nutzen wir eine nützliche Eigenschaft, dass eine Wahrscheinlichkeitsmaßnahme auf einem Produktraum das Produkt eines Wahrscheinlichkeitskernels und

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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