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

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 weakly coupled linear backward stochastic differential equations (BSDEs), and (a part of solution of BSDE) enter the state equations and cost functionals. Inspired by the stochastic control problem with partial information, we adopt the backward separation approach to solve the problem. By virtue of the stochastic maximum principle and optimal filter technique, we obtain a Hamiltonian system first, which is a fully coupled forward‐backward stochastic differential equation (FBSDE). And then, by 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.