Necessary/sufficient conditions for Pareto optimality in finite horizon mean-field type stochastic differential game
Necessary/sufficient conditions for Pareto optimality in finite horizon mean-field type stochastic differential game
复制标题
有限时域平均场型随机微分博弈帕累托最优的充要条件
DOI：
10.1016/j.automatica.2020.108951
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发表时间：
2020-09
期刊：
影响因子：
6.4
通讯作者：
Yaning Lin
中科院分区：
文献类型：
--
作者：
Yaning Lin
研究有限视界平均场型随机合作微分对策Pareto解存在的充分必要条件。基于Pareto最优的等价特征，将该问题转化为一组具有特殊结构的约束平均场型随机最优控制问题。利用平均场型随机最小值原理，提出了求解的必要条件。在某些凸假设下，证明了必要条件也是充分条件。其次，研究了不定线性二次（LQ）情况。指出两个相关的广义微分Riccati方程（GDREs）的可解性提供了帕累托有效策略等价于加权和最优控制的充分条件。此外，所有的Pareto解都是基于两个广义微分Lyapunov方程（gdle）的解得到的。最后通过一个算例说明了理论结果的有效性。
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.
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