BSDE Approach for α-Potential Stochastic Differential Games

2025/07/17 by Xin Dong Guo, Xun Li, Guo, Xin +3
Decision Sciences · Economics, Econometrics and Finance · #FOS: Mathematics #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Probability (math.PR) #Simulation Techniques and Applications #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2507.13256

openalex publication_date 2025/07/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

In this paper, we examine a class of α-potential stochastic differential games with random coefficients via the backward stochastic differential equations (BSDEs) approach. Specifically, we show that the first and second order linear derivatives of the objective function for each player can be expressed through the corresponding first and second-order adjoint equations, which leads to rigorous estimates for α. We illustrate the dependence of α on game characteristics through detailed analysis of linear-quadratic games, and with common noise.

Citations

• Imagined Potential Games: A Framework for Simulating, Learning and Evaluating Interactive Behaviors
• Multi-agent Reach-avoid MDP via Potential Games and Low-rank Policy Structure
• Towards An Analytical Framework for Dynamic Potential Games
• Independent and Decentralized Learning in Markov Potential Games
• Independent Policy Gradient for Large-Scale Markov Potential Games: Sharper Rates, Function Approximation, and Game-Agnostic Convergence
• Global Convergence of Multi-Agent Policy Gradient in Markov Potential Games
• Learning Parametric Closed-Loop Policies for Markov Potential Games
• Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics

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