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Linearly Solvable Continuous-Time General-Sum Stochastic Differential Games

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  • Monika Tomar
  • Takashi Tanaka

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.

Suggested Citation

  • Monika Tomar & Takashi Tanaka, 2026. "Linearly Solvable Continuous-Time General-Sum Stochastic Differential Games," Papers 2604.07479, arXiv.org.
    • Handle: RePEc:arx:papers:2604.07479
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    File URL: http://arxiv.org/pdf/2604.07479
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