发表机构
The Hong Kong Polytechnic University; Renmin University of China（香港理工大学; 中国人民大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文作为前期开环控制研究的延续，采用BSDE方法研究闭环α-势SDG，推导了参数α的精确估计，得到N个异构智能体博弈下最小势近似误差的N一致上界，该闭环界含反馈贡献且α未必趋近于0。
AI 中文摘要
本文作为我们前期开环控制研究（见文献[GLZ2025]）的延续，研究闭环α-势随机微分博弈（SDG）问题。通过运用倒向随机微分方程（BSDE）方法，我们推导了参数α的精确估计值。与我们早期的工作[GLZ2025]相比，本研究纳入了一阶和二阶敏感性状态过程，以及控制过程的敏感性。本研究的一个显著特征是，在涉及平均场型相互作用的N个异构智能体博弈背景下，我们推导了最小势近似误差的N一致上界。与相应的开环估计相比，闭环界包含了由反馈引起的、不会随N消失的贡献。因此，我们当前的估计通常不能保证α趋近于0。
英文摘要
In this paper, we study the closed-loop $α$-potential stochastic differential game (SDG) problem as a continuation of our prior research on open-loop control (see \cite{GLZ2025}). By utilizing the backward stochastic differential equation (BSDE) approach, we derive a precise estimate for the parameter $α$. Compared to our earlier work \cite{GLZ2025}, this study incorporates both first- and second-order sensitivity state processes, as well as the sensitivity of the control process. A distinguishing feature of this work is that, in the context of $N$-player heterogeneous agent games involving mean-field type interactions, we derive an $N$-uniform upper bound for the minimal potential approximation error. In contrast to the corresponding open-loop estimates, the closed-loop bound contains feedback-induced contributions that need not vanish with $N$. Consequently, our present estimate does not in general guarantee $α\rightarrow 0$.
