论文标题
Stackelberg随机差异游戏，具有不对称的嘈杂观测
Stackelberg Stochastic Differential Game with Asymmetric Noisy Observations
论文作者
论文摘要
本文关注的是一款具有不对称嘈杂的观察的Stackelberg随机差异游戏，其中一位追随者和一名领导者。在我们的模型中，追随者无法直接观察状态过程，但可以观察到嘈杂的观察过程，而领导者可以完全观察国家过程。考虑了开环stackelberg平衡。追随者首先通过部分观察解决了随机的最佳控制问题，获得了最大原理和验证定理。然后，领导者转向解决条件均值的前向后随机微分方程的最佳控制问题，并证明了最大原理和验证定理。讨论了带有不对称嘈杂观察的线性季节stackelberg随机差异游戏，以说明本文的理论结果。借助某些Riccati方程，开环的stackelberg平衡承认其状态估计反馈表示。
This paper is concerned with a Stackelberg stochastic differential game with asymmetric noisy observation, with one follower and one leader. In our model, the follower cannot observe the state process directly, but could observe a noisy observation process, while the leader can completely observe the state process. Open-loop Stackelberg equilibrium is considered. The follower first solve an stochastic optimal control problem with partial observation, the maximum principle and verification theorem are obtained. Then the leader turns to solve an optimal control problem for a conditional mean-field forward-backward stochastic differential equation, and both maximum principle and verification theorem are proved. An linear-quadratic Stackelberg stochastic differential game with asymmetric noisy observation is discussed to illustrate the theoretical results in this paper. With the aid of some Riccati equations, the open-loop Stackelberg equilibrium admits its state estimate feedback representation.
