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arXiv · 2609.12687

Extended Mean Field Control Games with Moment Interactions: General Framework and Linear-Quadratic Model

Zhongyuan Cao·Mathieu Laurière·Andrew Shi·Jiefei Yang
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Abstract

Mean field control games (MFCGs) provide a framework for studying non-cooperative games involving groups of cooperative players in the limit as both the number of players and the number of groups go to infinity.This class of games includes mean field games (MFGs) and mean field control (MFC) problems as special cases, corresponding to purely non-cooperative and purely cooperative settings, respectively. We incorporate interactions through the mean of actions, hence the terminology of extended MFCGs. We first show that the equilibrium control can be described using a coupled system of partial differential equations consisting of a Hamilton-Jacobi-Bellman equation and a Fokker-Planck equation. After introducing the general framework, we focus on a linear-quadratic (LQ) structure. We show that the equilibrium can be reduced to a system of ODEs, generalizing those obtained for MFGs and MFC problems. We then provide two numerical examples illustrating specific features of MFCGs.

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Zhongyuan Cao, Mathieu Laurière, Andrew Shi, Jiefei Yang. 2026-09-11. Extended Mean Field Control Games with Moment Interactions: General Framework and Linear-Quadratic Model. https://arxiv.org/abs/2609.12687

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