Pareto efficiency of infinite-horizon cooperative stochastic differential games with Markov jumps and Poisson jumps

Abstract

This paper investigates a wide class of infinite-horizon cooperative stochastic differential games with Markov jumps and Poisson jumps, which can model uncertainties of internal mode transition and characterize occasional sudden changes in the games, respectively. Firstly, the necessary conditions which guarantee the existence of Pareto solutions are obtained by utilizing the Lagrange multiplier method and the stochastic maximum principle with Markov jumps and Poisson jumps. Then the sufficient conditions which guarantee the existence of Pareto efficient strategies are derived. Secondly, the well-posedness of cooperative stochastic differential games (CSDG) with Markov jumps and Poisson jumps in infinite horizon is established when the solution of generalized algebraic Riccati equation (GARE) exists. Furthermore, we can obtain Pareto solutions by introducing the coupled algebraic Lyapunov equations (ALEs). Finally, the numerical examples verify the theoretical results.