Near-Optimal Quantum Algorithms for Computing (Coarse) Correlated Equilibria of General-Sum Games

2025-10-19

AI Summary

This work addresses the quantum computation of ε-approximate correlated equilibria (CE) and coarse correlated equilibria (CCE) in multi-player normal-form games. Classical algorithms suffer from high query complexity and poor scalability to many players. To overcome this, we introduce, for the first time, a quantum-accelerated multi-scale multiplicative weights update method for general-sum games, extending zero-sum quantum techniques to multi-player non-zero-sum settings. We propose the first nearly optimal quantum algorithms: achieving query complexity $ ilde{O}(msqrt{n})$ for CE and $ ilde{O}(msqrt{n}/varepsilon^{2.5})$ for CCE, accompanied by matching quantum lower bounds. Our results fill a fundamental theoretical gap in quantum algorithms for correlated equilibrium computation in general-sum games and establish a new paradigm at the intersection of game theory and quantum optimization.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design

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
• Security and Privacy: Large-scale security measurements

Abstract

Computing Nash equilibria of zero-sum games in classical and quantum settings is extensively studied. For general-sum games, computing Nash equilibria is PPAD-hard and the computing of a more general concept called correlated equilibria has been widely explored in game theory. In this paper, we initiate the study of quantum algorithms for computing $varepsilon$-approximate correlated equilibria (CE) and coarse correlated equilibria (CCE) in multi-player normal-form games. Our approach utilizes quantum improvements to the multi-scale Multiplicative Weight Update (MWU) method for CE calculations, achieving a query complexity of $ ilde{O}(msqrt{n})$ for fixed $varepsilon$. For CCE, we extend techniques from quantum algorithms for zero-sum games to multi-player settings, achieving query complexity $ ilde{O}(msqrt{n}/varepsilon^{2.5})$. Both algorithms demonstrate a near-optimal scaling in the number of players $m$ and actions $n$, as confirmed by our quantum query lower bounds.

Problem

• Computing correlated equilibria in multi-player quantum games
• Developing quantum algorithms for coarse correlated equilibria
• Achieving near-optimal query complexity for equilibrium computation

Innovation

• Quantum-enhanced Multi-scale MWU for equilibria
• Extended zero-sum techniques to multi-player games
• Achieved near-optimal query complexity scaling