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

Mukesh Ghimire, Zhe Xu, Yi Ren

Keywords: Differential Game, Incomplete Information Game

TL;DR: This work 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 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 [github](https://github.com/ghimiremukesh/cams/tree/workshop).

Submission Number: 12