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.

本文研究了有限水平均值场型随机合作微分对策中存在帕累托解的充要条件。基于帕累托最优的等效刻画，将该问题转化为一组具有特殊结构的约束均值场型随机最优控制问题。利用均值场型随机最小原理，提出了必要条件。在某些凸假设下，证明必要条件也是充分条件。接下来，研究不定线性二次（LQ）情况。要指出的是，两个相关的广义微分里卡提方程（GDRE）的可解性提供了一个充分的条件，在此条件下，帕累托有效策略等同于加权和最优控制。此外，所有的Pareto解都是基于两个广义微分Lyapunov方程（GDLE）的解获得的。最后，通过实例说明了理论结果的有效性。