General Leader-Follower Linear-Quadratic Stochastic Graphon Games with Indefinite Control Weights
Abstract
This paper studies general leader-follower linear-quadratic stochastic graphon games with indefinite control weights. The model consists of one leader and a continuum of followers, where the followers interact through graphon aggregate terms and are coupled with the leader through their dynamics and cost functionals. Compared with existing related models, the state equations considered here allow more general diffusion terms, including diffusion coefficients depending on the states, controls, leader variables, and graphon aggregate terms. Using the stochastic maximum principle, we characterize the followers' Nash response and the leader's optimal control through coupled forward-backward stochastic systems with graphon aggregate terms. Under suitable Riccati solvability and convexity conditions, we construct a Stackelberg-Nash equilibrium for the limiting graphon game. We further design decentralized strategies for the associated finite-player network game and prove that they form an approximate Stackelberg-Nash equilibrium, which yields a propagation of chaos result. The framework covers, as special cases, indefinite linear-quadratic stochastic graphon games, Stackelberg mean field games, and stochastic graphon games with random effects.
Related
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BibTeX
@misc{chen2026general,
title = {{General Leader-Follower Linear-Quadratic Stochastic Graphon Games with Indefinite Control Weights}},
author = {Weijia Chen and Jingtao Shi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24185},
eprint = {2609.24185},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24185},
note = {CC0},
}
RIS
TY - UNPB
TI - General Leader-Follower Linear-Quadratic Stochastic Graphon Games with Indefinite Control Weights
AU - Weijia Chen
AU - Jingtao Shi
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24185
UR - https://arxiv.org/abs/2609.24185
AB - This paper studies general leader-follower linear-quadratic stochastic graphon games with indefinite control weights. The model consists of one leader and a continuum of followers, where the followers interact through graphon aggregate terms and are coupled with the leader through their dynamics and cost functionals. Compared with existing related models, the state equations considered here allow more general diffusion terms, including diffusion coefficients depending on the states, controls, leader variables, and graphon aggregate terms. Using the stochastic maximum principle, we characterize the followers' Nash response and the leader's optimal control through coupled forward-backward stochastic systems with graphon aggregate terms. Under suitable Riccati solvability and convexity conditions, we construct a Stackelberg-Nash equilibrium for the limiting graphon game. We further design decentralized strategies for the associated finite-player network game and prove that they form an approximate Stackelberg-Nash equilibrium, which yields a propagation of chaos result. The framework covers, as special cases, indefinite linear-quadratic stochastic graphon games, Stackelberg mean field games, and stochastic graphon games with random effects.
ER -