Incomplete Information Linear-Quadratic Mean-Field Games and Related Riccati Equations
Abstract
We study a class of linear-quadratic mean-field games with incomplete information. For each agent, the state is given by a linear forward stochastic differential equation with common noise. Moreover, both the state and control variables can enter the diffusion coefficients of the state equation. We deduce the open-loop adapted decentralized strategies and feedback decentralized strategies by mean-field forward-backward stochastic differential equation and Riccati equations, respectively. The well-posedness of the corresponding consistency condition system is obtained and the limiting state-average turns out to be the solution of a mean-field stochastic differential equation driven by common noise. We also verify the -Nash equilibrium property of the decentralized control strategies. Finally, a network security problem is studied to illustrate our results as an application.
Keywords
Cite
@article{arxiv.2307.01005,
title = {Incomplete Information Linear-Quadratic Mean-Field Games and Related Riccati Equations},
author = {Min Li and Tianyang Nie and Shunjun Wang and Ke Yan},
journal= {arXiv preprint arXiv:2307.01005},
year = {2023}
}