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

TL;DR

This paper introduces a scalable method for computing equilibrium strategies in two-player zero-sum differential games with continuous action spaces and one-sided information, leveraging convexification and Isaacs' condition.

Contribution

It presents a novel approach that achieves complexity independent of action space size and decouples strategy computation under one-sided information.

Findings

Algorithm effectively approximates optimal strategies in homing games.

Complexity is independent of action space size due to convexification.

Decoupling of strategies simplifies computation in one-sided information scenarios.

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