Two-Player Zero-Sum Differential Games with One-Sided Information and Continuous Actions

Mukesh Ghimire, Lei Zhang, Zhe Xu, Yi Ren

Keywords: Incomplete Information Game, Differential Game

TL;DR: This paper highlights the limitations of existing state-of-the-art methods for solving one-sided incomplete information games with continuous actions and introduces an algorithm that approximates mixed strategies in such games.

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 "Cav u" property of behavioral strategies in incomplete-information games and the Isaacs' condition that commonly holds for control systems, and that (2) the computation of the two equilibrium strategies can be decoupled under the Isaacs' condition. We provide computational complexity of the resultant algorithm for approximating continuous-action mixed strategies (CAMS). Empirically, we demonstrate correctness of CAMS using a homing game where the Nash equilibrium exists analytically, and scalability through the same game with higher-dimensional actions. Codes available in [anonymous repo](https://anonymous.4open.science/r/iclr-3245).

Primary Area: learning theory

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Submission Number: 3245