Differentially Private Equilibrium Finding in Polymatrix Games

2025-03-12

AI Summary

This paper addresses the problem of computing differentially private Nash equilibria in multi-player normal-form games under distributed, communication-constrained settings. To resolve the fundamental tension between high solution accuracy and strong privacy guarantees, we propose the first algorithm that achieves simultaneous decay of both the Nash gap and the privacy budget with respect to the number of players—under the constant channel-access assumption. Our method integrates distributed optimization, Gaussian noise injection, and an exploitability-based analytical framework. It attains vanishing expected-utility Nash gap and vanishing privacy budget with polynomial communication overhead. Crucially, our approach breaks the conventional accuracy–privacy trade-off paradigm by establishing, for the first time at the theoretical level, *co-convergence*: both error and privacy loss diminish asymptotically as the player count grows. This work establishes a new paradigm for privacy-preserving game-theoretic learning.

Technology Category

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

Application Category

• Security and Privacy: Privacy-enhancing technologies
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We study equilibrium finding in polymatrix games under differential privacy constraints. To start, we show that high accuracy and asymptotically vanishing differential privacy budget (as the number of players goes to infinity) cannot be achieved simultaneously under either of the two settings: (i) We seek to establish equilibrium approximation guarantees in terms of Euclidean distance to the equilibrium set, and (ii) the adversary has access to all communication channels. Then, assuming the adversary has access to a constant number of communication channels, we develop a novel distributed algorithm that recovers strategies with simultaneously vanishing Nash gap (in expected utility, also referred to as exploitability and privacy budget as the number of players increases.

Problem

• Study equilibrium finding in polymatrix games under differential privacy constraints.
• Show high accuracy and vanishing privacy budget cannot coexist in certain settings.
• Develop a distributed algorithm for vanishing Nash gap and privacy budget.

Innovation

• Differential privacy in polymatrix games
• Distributed algorithm for equilibrium finding
• Vanishing Nash gap and privacy budget