Graphexon Mean Field Games on Large Network Limits
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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BibTeX
@misc{caines2026graphexon,
title = {{Graphexon Mean Field Games on Large Network Limits}},
author = {Peter E. Caines and Minyi Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27292},
eprint = {2610.27292},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27292},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Graphexon Mean Field Games on Large Network Limits
AU - Peter E. Caines
AU - Minyi Huang
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27292
UR - https://arxiv.org/abs/2610.27292
AB - 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.
ER -