Individual and mass behavior in large population forward–backward stochastic control problems: Centralized and Nash equilibrium solutions
Individual and mass behavior in large population forward–backward stochastic control problems: Centralized and Nash equilibrium solutions
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DOI：
10.1002/oca.2727
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发表时间：
2021-04
影响因子：
1.8
通讯作者：
Shujun Wang;Hua Xiao
中科院分区：
文献类型：
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作者：
Shujun Wang;Hua Xiao
本文研究了一类大群体系统的动态优化，其中大量可忽略不计的智能体通过状态平均在其成本函数和状态动力学中耦合。我们的设置中最重要的特征是单个代理的动态是通过前向-后向随机微分方程建模的。相关的平均场博弈，在其前向-后向意义上，也是为了寻求分散策略而制定的。与前向情况不同，我们的前向-后向平均场博弈的一致性条件涉及五个 Riccati 和力率方程。此外，它们的初始条件和终止条件是混合的，因此这里应用了一些特殊的解耦技术。我们还验证了派生的去中心化策略的ε-纳什均衡特性。为此，采用了对后向随机系统的一些估计。
This article studies a class of dynamic optimization of large‐population system in which a large number of negligible agents are coupled via state‐average in their cost functional and state dynamics. The most significant feature in our setup is the dynamics of individual agents are modeled by forward–backward stochastic differential equations. The associated mean‐field game, in its forward–backward sense, is also formulated to seek the decentralized strategies. Unlike the forward case, the consistency conditions of our forward–backward mean‐field games involve five Riccati and force rate equations. Moreover, their initial and terminal conditions are mixed thus some special decoupling technique is applied here. We also verify the ε ‐Nash equilibrium property of the derived decentralized strategies. To this end, some estimates to backward stochastic system are employed.