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

2025-02-07

AI Summary

This work addresses two-player zero-sum differential games with continuous action spaces under one-sided information, aiming to overcome the computational intractability of conventional no-regret algorithms in high-dimensional physical systems. We propose the first decoupled framework that integrates the convexification structure of incomplete-information games with the Isaacs partial differential equation (PDE) conditions, decomposing equilibrium policy computation into two independent convex optimization subproblems—thereby rendering computational complexity independent of action-space dimensionality. Leveraging differential game theory, convex optimization, and numerical dynamic programming, we design a scalable approximate algorithm that efficiently approximates optimal strategies. The method is validated on the homing game—a canonical pursuit-evasion problem—demonstrating significant improvements in both scalability and solution quality. Our implementation is publicly available.

Technology Category

• Search and Optimization: Adversarial Search
• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Adversarial Agents

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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

Problem

• Addresses complexity in continuous action spaces
• Solves two-player zero-sum games with one-sided information
• Develops algorithm for optimal strategy approximation

Innovation

• Continuous action space optimization
• Convexification of incomplete-information games
• Decoupling equilibrium strategies computation