Linear-quadratic mean-field game for stochastic large-population systems with jump diffusion

This study is concerned with linear-quadratic mean-field game problem for a class of stochastic large-population systems with Poisson processes. The control is allowed to enter the jump diffusion terms of the individuals' state equation. By virtue of the stochastic Hamiltonian system and Riccati equation for limiting control problem, the decentralised optimal strategies are represented in the open-loop and closed-loop forms, respectively. Different from the existing results, the limit representation of average term is proposed in closed-loop form via the separation technique. Meanwhile, the decentralised optimal strategies are verified to be the epsilon-Nash equilibrium of the original problem. Finally, two practical control problems in engineering and economics areas are presented to demonstrate the good performance of theoretical results.