Limit Theory for N-Player α-Potential Games
Abstract
The recently introduced framework of α-potential games facilitates the analysis of finite-player dynamic games by reducing the search for approximate Nash equilibria to the minimization of a single α-potential function. In this work, we show that the approximate potential structure of finite-player games persists in the large-population limit, leading naturally to a notion of α-potential mean field games (MFGs). Specifically, we show that both the optimal values and the minimizers of normalized N-player αN-potential functions converge to those of a mean field control (MFC) problem with measure-valued controls. We identify the objective of this limiting MFC problem as an α∞-potential function for an MFG, and characterize the parameter α∞ analytically. We further show that limN→∞αN= 0 is equivalent to standard conditions for potential MFGs, in which case the limiting MFC objective becomes a potential function for the MFG. Together, these results provide new constructions of potential MFGs from finite-player games through the asymptotic condition limN→ ∞αN= 0, and establish propagation of chaos of potential-selected equilibria from N-player games to MFGs with general controlled diffusions, common noise, and non-separable state-control interactions.
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BibTeX
@misc{guo2026limit,
title = {{Limit Theory for $N$-Player $α$-Potential Games}},
author = {Xin Guo and Meng Wang and Yufei Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.09815},
eprint = {2606.09815},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.09815},
}
RIS
TY - UNPB
TI - Limit Theory for N-Player α-Potential Games
AU - Xin Guo
AU - Meng Wang
AU - Yufei Zhang
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2606.09815
UR - https://arxiv.org/abs/2606.09815
AB - The recently introduced framework of α-potential games facilitates the analysis of finite-player dynamic games by reducing the search for approximate Nash equilibria to the minimization of a single α-potential function. In this work, we show that the approximate potential structure of finite-player games persists in the large-population limit, leading naturally to a notion of α-potential mean field games (MFGs). Specifically, we show that both the optimal values and the minimizers of normalized N-player α_N-potential functions converge to those of a mean field control (MFC) problem with measure-valued controls. We identify the objective of this limiting MFC problem as an α_∞-potential function for an MFG, and characterize the parameter α_∞ analytically. We further show that lim_N→∞α_N= 0 is equivalent to standard conditions for potential MFGs, in which case the limiting MFC objective becomes a potential function for the MFG. Together, these results provide new constructions of potential MFGs from finite-player games through the asymptotic condition lim_N→ ∞α_N= 0, and establish propagation of chaos of potential-selected equilibria from N-player games to MFGs with general controlled diffusions, common noise, and non-separable state-control interactions.
ER -