Closed-loop α-Potential Stochastic Differential Games via a BSDE Approach
Abstract
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→ 0.
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BibTeX
@misc{li2026closedloop,
title = {{Closed-loop $α$-Potential Stochastic Differential Games via a BSDE Approach}},
author = {Xun Li and Liangquan Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09756},
eprint = {2609.09756},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09756},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Closed-loop α-Potential Stochastic Differential Games via a BSDE Approach
AU - Xun Li
AU - Liangquan Zhang
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09756
UR - https://arxiv.org/abs/2609.09756
AB - 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→ 0.
ER -