Pareto-based Stackelberg differential game for stochastic systems with multi-followers

This paper is concerned about a Pareto-based Stackelberg stochastic differential game with multi-followers, in which followers are cooperative relations. First of all, necessary and sufficient conditions for the existence of Pareto-based Stackelberg equilibrium are given for the general Pareto-based Stackelberg stochastic differential game problem. Next, we study the above game problem in the linear-quadratic (LQ) case and obtain a feedback form of Pareto-based Stackelberg equilibrium. The solvability of Riccati equations is guaranteed under some assumptions. Finally, the theoretical results are used to solve a national debt management problem.