标题： BSDE方法用于$α$-势随机微分博弈 显示英文标题

标题： BSDE Approach for $α$-Potential Stochastic Differential Games

摘要： 在本文中，我们通过后向随机微分方程（BSDEs）方法研究了一类具有随机系数的$\alpha$型随机微分博弈。 具体而言，我们证明了每个玩家的目标函数的一阶和二阶线性导数可以通过相应的第一和二阶伴随方程来表示，这导致了对$\alpha$的严格估计。 我们通过线性二次博弈以及共同噪声的详细分析，说明了$\alpha$对博弈特征的依赖性。 显示英文摘要

摘要： In this paper, we examine a class of $\alpha$-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 $\alpha$. We illustrate the dependence of $\alpha$ on game characteristics through detailed analysis of linear-quadratic games, and with common noise.