A linear-quadratic mean-field game of backward stochastic differential equation with partial information and common noise

Pengyan Huang, Guangchen Wang, Wencan Wang and Yu Wang

Applied Mathematics and Computation, 2023, vol. 446, issue C

Abstract: This paper studies a linear-quadratic (LQ) mean-field game of stochastic large-population system with partial information and common noise, where the large-population system satisfies a class of backward stochastic differential equations (BSDEs), and both coupling structure and ki (a part of solution of BSDE) enter state equations and cost functionals. By virtue of stochastic maximum principle and optimal filter technique, we obtain a Hamiltonian system first, which is a fully-coupled forward-backward stochastic differential equation (FBSDE). Decoupling the Hamiltonian system, we obtain three ordinary differential equations (ODEs), a forward and a backward optimal filtering equations, which enable us to derive an optimal control of an auxiliary limiting control problem. Next, we verify that a decentralized control strategy is an ϵ-Nash equilibrium of the LQ game. Finally, we solve a product pricing problem and a network security control problem in applications. We give a near-optimal price strategy and a near-optimal control strategy with numerical simulations, respectively.

Keywords: Backward stochastic differential equation; Large-population system; Mean-field game; Optimal filter; ϵ-Nash equilibrium (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:446:y:2023:i:c:s0096300323000681

DOI: 10.1016/j.amc.2023.127899

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