Zero-Error Nash Equilibrium: Harnessing Nonlocal Correlation in Incomplete Information Games

2025-09-02

AI Summary

In incomplete-information games, classical private information cannot support Nash equilibria with zero error probability. This work introduces the concept of *zero-error correlated Nash equilibrium*, unifying Shannon’s zero-error communication, Bayesian games, and Bell nonlocality. We demonstrate that quantum entanglement—particularly genuine multipartite entanglement—exceeds classical coordination limits: we construct a three-player Bayesian game achieving zero-error coordination, and show that all two-qubit pure entangled states (except maximally entangled ones) enable strictly stronger coordination than classical strategies. Furthermore, under experimentally realistic noisy conditions, nonlocal correlations sustain near-zero-error decision-making. This work establishes, for the first time, a systematic theoretical framework treating quantum nonlocality as a coordination resource, thereby providing a new paradigm for reliable distributed decision-making under uncertainty.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Claude Shannon's zero-error communication paradigm reshaped our understanding of fault-tolerant information transfer. Here, we adapt this notion into game theory with incomplete information. We ask: can players with private information coordinate on a Nash equilibrium with zero probability of error? We identify Bayesian games in which such coordination is impossible classically, yet achievable by harnessing Bell nonlocal correlations. We formalize this requirement as zero-error Nash equilibrium coordination, establishing a new bridge between information theory, game theory, and quantum nonlocality. Furthermore, we construct a tripartite Bayesian game that admits zero-error Nash equilibrium coordination with genuine entanglement, and a two-player game where a stronger notion of coordination can be achieved using every two-qubit pure entangled state except the maximally one. Crucially, the advantage persists under experimentally relevant noise, demonstrating nonlocality as a robust resource for near-zero error decision-making under uncertainty.

Problem

• Zero-error Nash equilibrium coordination in Bayesian games
• Classical impossibility versus quantum nonlocality advantage
• Robust nonlocal resource for near-zero error decision-making

Innovation

• Using Bell nonlocal correlations for Nash equilibrium
• Formalizing zero-error Nash equilibrium coordination concept
• Leveraging entanglement for robust decision-making under noise