Closed-loop $\alpha$-Potential Stochastic Differential Games via a BSDE Approach

Xun Li; Liangquan Zhang

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arXiv · 2609.09756

Closed-loop $\alpha$-Potential Stochastic Differential Games via a BSDE Approach

Xun Li·Liangquan Zhang

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Abstract

In this paper, we study the closed-loop $\alpha $-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 $\alpha $. 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 $\alpha \rightarrow 0$.

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BibTeX RIS

Xun Li, Liangquan Zhang. 2026-09-09. Closed-loop $\alpha$-Potential Stochastic Differential Games via a BSDE Approach. https://arxiv.org/abs/2609.09756

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