Mean Field Games With Parametrized Followers
Mean Field Games With Parametrized Followers
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DOI：
10.1109/tac.2019.2910945
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发表时间：
2020-01
影响因子：
6.8
通讯作者：
A. Bensoussan;T. Cass;M. Chau;S. Yam
中科院分区：
文献类型：
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作者：
A. Bensoussan;T. Cass;M. Chau;S. Yam
我们认为，平均场游戏之间的主导领导者和许多追随者，这样每个追随者是受到异质延迟效应的领导者的行动，谁又可以行使治理人口通过这种影响力。延迟效应被假定为离散分布的追随者。给定足够的正则系数，我们描述了一个系统的正倒向随机微分方程和随机偏微分方程的平衡点的解的存在性的必要条件。我们提供了一个深入的研究，为特定的线性二次的情况下。采用泛函方法，得到了保证整个平均场对策问题解唯一存在的与时间无关的充分条件。几个不同的时间范围和人口的数值插图证明。
We consider mean field games between a dominant leader and many followers, such that each follower is subject to a heterogeneous delay effect from the leader's action, who in turn can exercise governance on the population through this influence. The delay effects are assumed to be discretely distributed among the followers. Given regular enough coefficients, we describe a necessary condition for the existence of a solution for the equilibrium by a system of coupled forward–backward stochastic differential equations and stochastic partial differential equations. We provide a thorough study for the particular linear quadratic case. By adopting a functional approach, we obtain the time-independent sufficient condition, which warrants the unique existence of the solution of the whole mean field game problem. Several numerical illustrations with different time horizons and populations are demonstrated.