This paper introduces a class of continuous-time, finite-player stochastic general-sum differential games that admit solutions through an exact linear PDE system. We formulate a distribution planning game utilizing the cross-log-likelihood ratio to naturally model multi-agent spatial conflicts, such as congestion avoidance. By applying a generalized multivariate Cole-Hopf transformation, we decouple the associated non-linear Hamilton-Jacobi-Bellman (HJB) equations into a system of linear partial differential equations. This reduction enables the efficient, grid-free computation of feedback Nash equilibrium strategies via the Feynman-Kac path integral method, effectively overcoming the curse of dimensionality.

翻译：本文介绍了一类连续时间、有限参与者的随机一般和微分博弈，该类博弈可通过精确线性偏微分方程组求解。我们利用交叉对数似然比构建了一种分布规划博弈，以自然建模多智能体空间冲突（如拥塞避免）。通过应用广义多元Cole-Hopf变换，我们将相关的非线性Hamilton-Jacobi-Bellman (HJB) 方程解耦为线性偏微分方程组。这一简化使得能够通过Feynman-Kac路径积分方法高效、无网格地计算反馈纳什均衡策略，从而有效克服维度灾难。