Linearly Solvable Continuous-Time General-Sum Stochastic Differential Games
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918435708993536 |
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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 |