Decentralized Strategies for Backward Linear-Quadratic Mean Field Games and Teams

2025/01/02 by Yu Si, Si, Yu, Jingtao Shi +1 · 1 citation
Economics, Econometrics and Finance · Engineering · #49K45 #49N70 #60H10 #91A23 #93E20 #FOS: Mathematics #Game Theory and Voting Systems #Guidance and Control Systems #Optimization and Control (math.OC) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2501.04717

openalex publication_date 2025/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies a new class of linear-quadratic mean field games and teams problem, where the large-population system satisfies a class of N weakly coupled linear backward stochastic differential equations (BSDEs), and z_i (a part of solution of BSDE) enter the 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 derive a feedback form optimal strategy by introducing Riccati equations, stochastic differential equation (SDE) and BSDE. Finally, we provide a numerical example to simulate our results.

Cited by

• General Linear-Quadratic Mean Field Stochastic Differential Game with Common Noise: A Direct Method

Related

• Backward Linear-Quadratic Mean Field Stochastic Differential Games: A Direct Method
• Mean Field Linear-Quadratic-Gaussian (LQG) Games of Forward-Backward Stochastic Differential Equations
• Mean Field Linear-Quadratic-Gaussian (LQG) Games: Major and Minor Players
• Direct Approach of Linear-Quadratic Stackelberg Mean Field Games of Backward-Forward Stochastic Systems
• Linear-Quadratic Mean Field Games with Common Noise: A Direct Approach