Pareto efficiency of finite-horizon mean-field cooperative stochastic differential games with poisson jumps

Abstract

This paper investigates finite-horizon mean-field cooperative stochastic differential games (CSDG) with Poisson jumps. The game model can describe the case where the game has external disturbances and suffers sudden changes. First, for the fixed initial state, the necessary conditions which guarantee the existence of Pareto solutions can be obtained by utilizing the Lagrange multiplier method and the mean-field type stochastic maximum principle (MF-SMP) with Poisson jumps. Then, the sufficient conditions which guarantee the existence of Pareto efficient strategies are derived. Next, for any initial states, the well-posedness of finite-horizon mean-field CSDG with Poisson jumps is established under the assumption that the solution of generalized algebraic Riccati equations (GAREs) exists. Further, all Pareto solutions can be obtained by constructing an algebraic Lyapunov equations (ALEs). Finally, a numerical example given illustrates our results.