标题：Necessary/sufficient conditions for Pareto optimality in finite horizon mean-field type stochastic differential game
作者机构：[Lin, Yaning] Shandong Univ Technol, Sch Math & Stat, Zibo 255000, Peoples R China.
通讯作者地址：Lin, YN (corresponding author), Shandong Univ Technol, Sch Math & Stat, Zibo 255000, Peoples R China.
关键词：Pareto optimality; Mean-field type stochastic systems; Cooperative; differential game; LQ mean-field type stochastic optimal control theory
摘要：This paper is concerned with necessary and sufficient conditions for the existence of Pareto solutions in finite horizon mean-field type stochastic cooperative differential game. Based on the equivalent characterization of Pareto optimality, the problem is transformed into a set of constrained mean-field type stochastic optimal control problems with a special structure. Utilizing the mean-field type stochastic minimum principle, the necessary conditions are put forward. Under certain convex assumptions, it is shown that the necessary conditions are also sufficient ones. Next, the indefinite linear quadratic (LQ) case is studied. It is pointed out that the solvability of two related generalized differential Riccati equations (GDREs) provides a sufficient condition under which Pareto efficient strategies are equivalent to weighted sum optimal controls. In addition, all Pareto solutions are obtained based on the solutions of two generalized differential Lyapunov equations (GDLEs). At last, an example sheds light on the effectiveness of the theoretical results. (C) 2020 Published by Elsevier Ltd.