Linearly Solvable Continuous-Time General-Sum Stochastic Differential Games

Fuente: arXiv
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Main Authors: Tomar, Monika, Tanaka, Takashi
Format: Preprint
Published: 2026
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author Tomar, Monika
Tanaka, Takashi
author_facet Tomar, Monika
Tanaka, Takashi
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2604_07479
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Linearly Solvable Continuous-Time General-Sum Stochastic Differential Games
Tomar, Monika
Tanaka, Takashi
Optimization and Control
Computer Science and Game Theory
Systems and Control
Theoretical Economics
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.
title Linearly Solvable Continuous-Time General-Sum Stochastic Differential Games
topic Optimization and Control
Computer Science and Game Theory
Systems and Control
Theoretical Economics
url https://arxiv.org/abs/2604.07479