Linearly Solvable Continuous-Time General-Sum Stochastic Differential Games
Optimization and Control
2026-04-10 v1 Computer Science and Game Theory
Systems and Control
Theoretical Economics
Systems and Control
Abstract
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.
Keywords
Cite
@article{arxiv.2604.07479,
title = {Linearly Solvable Continuous-Time General-Sum Stochastic Differential Games},
author = {Monika Tomar and Takashi Tanaka},
journal= {arXiv preprint arXiv:2604.07479},
year = {2026}
}