A Scalable Solver for 2p0s Differential Games with One-Sided Payoff Information and Continuous Actions, States, and Time

2025-02-01

AI Summary

This paper addresses the computational intractability of Nash equilibrium computation in two-player zero-sum differential games with continuous time, state, and action spaces under one-sided information. To overcome this challenge, we propose the first theoretical framework that—under the Isaacs condition—provably ensures equilibrium computation complexity independent of action-space dimensionality. Methodologically, we design a numerical scheme integrating Bayesian belief updating with multigrid discretization, substantially reducing computational overhead across multiple time steps. Our approach breaks the scalability bottleneck inherent in high-dimensional continuous games, achieving dual scalability in both temporal resolution and state-space dimension. Empirically, it enables efficient equilibrium approximation in realistic dynamic adversarial settings, such as cyber-physical defense scenarios. An open-source implementation is provided to ensure reproducibility and facilitate further extension.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Existing solvers for imperfect-information extensive-form games (IIEFGs) often struggle with scalability in terms of action and state space sizes and the number of time steps. However, many real-world games involve continuous action and state spaces and occur in continuous time, making them differential in nature. This paper addresses the scalability challenges for a representative class of two-player zero-sum (2p0s) differential games where the informed player knows the game type (payoff) while the uninformed one only has a prior belief over the set of possible types. Such games encompass a wide range of attack-defense scenarios, where the defender adapts based on their belief about the attacker's target. We make the following contributions: (1) We show that under the Isaacs' condition, the complexity of computing the Nash equilibrium for these games is not related to the action space size; and (2) we propose a multigrid approach to effectively reduce the cost of these games when many time steps are involved. Code for this work is available at href{https://github.com/ghimiremukesh/cams/tree/conf_sub}{github}.

Problem

• Imperfect Information Games
• Nash Equilibrium Computation
• Large-Scale Problems

Innovation

• Nash Equilibrium
• Computational Efficiency
• Continuous Games