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arXiv · 2502.05314

Two-Player Zero-Sum Differential Games with One-Sided Information

Mukesh Ghimire·Zhe Xu·Yi Ren
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Abstract

Unlike Poker where the action space $\mathcal{A}$ is discrete, differential games in the physical world often have continuous action spaces not amenable to discrete abstraction, rendering no-regret algorithms with $\mathcal{O}(|\mathcal{A}|)$ complexity not scalable. To address this challenge within the scope of two-player zero-sum (2p0s) games with one-sided information, we show that (1) a computational complexity independent of $|\mathcal{A}|$ can be achieved by exploiting the convexification property of incomplete-information games and the Isaacs' condition that commonly holds for dynamical systems, and that (2) the computation of the two equilibrium strategies can be decoupled under one-sidedness of information. Leveraging these insights, we develop an algorithm that successfully approximates the optimal strategy in a homing game. Code available in https://github.com/ghimiremukesh/cams/tree/workshop

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Mukesh Ghimire, Zhe Xu, Yi Ren. 2025-02-07. Two-Player Zero-Sum Differential Games with One-Sided Information. https://arxiv.org/abs/2502.05314

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