A kind of linear‐quadratic Pareto cooperative differential game with partial information

Abstract

This article is concerned with a linear‐quadratic (LQ) Pareto cooperative differential game of stochastic differential equation (SDE) with partial information, where the control system is nonhomogeneous. First, we give the existence and uniqueness of solution to a new class of conditional mean‐field forward‐backward stochastic differential equations (CMF‐FBSDEs). Next, we obtain Pareto efficient strategies with a method of weighted sum optimization. It should be noted that the results depend on weight here. Feedback Pareto efficient strategies are obtained under some special information structure, and Pareto solutions are derived through six equations. Meanwhile, we give a characterization of optimal weight under stochastic case. Finally, the theoretical results are used to solve a kind of national income problem, and numerical simulations are given.