Differentially-private Distributed Algorithms for Aggregative Games with Guaranteed Convergence

TL;DR

This paper introduces a fully distributed, privacy-preserving algorithm for computing Nash equilibria in aggregative games, ensuring both rigorous differential privacy and high accuracy without sacrificing efficiency.

Contribution

It presents a novel, encryption-free, differentially-private distributed method that guarantees convergence and accuracy in aggregative games, even with stochastic estimates.

Findings

Achieves rigorous differential privacy with guaranteed convergence.

Effective even when adversaries access all shared information.

Applicable to stochastic aggregative games with accurate equilibrium computation.

Abstract

The distributed computation of a Nash equilibrium in aggregative games is gaining increased traction in recent years. Of particular interest is the mediator-free scenario where individual players only access or observe the decisions of their neighbors due to practical constraints. Given the competitive rivalry among participating players, protecting the privacy of individual players becomes imperative when sensitive information is involved. We propose a fully distributed equilibrium-computation approach for aggregative games that can achieve both rigorous differential privacy and guaranteed computation accuracy of the Nash equilibrium. This is in sharp contrast to existing differential-privacy solutions for aggregative games that have to either sacrifice the accuracy of equilibrium computation to gain rigorous privacy guarantees, or allow the cumulative privacy budget to grow unbounded, hence losing privacy guarantees, as iteration proceeds. Our approach uses independent noises across players, thus making it effective even when adversaries have access to all shared messages as well as the underlying algorithm structure. The encryption-free nature of the proposed approach, also ensures efficiency in computation and communication. The approach is also applicable in stochastic aggregative games, able to ensure both rigorous differential privacy and guaranteed computation accuracy of the Nash equilibrium when individual players only have stochastic estimates of their pseudo-gradient mappings. Numerical comparisons with existing counterparts confirm the effectiveness of the proposed approach.