An Efficient Distributed Nash Equilibrium Seeking with Compressed and Event-triggered Communication

TL;DR

This paper introduces an efficient distributed Nash equilibrium seeking algorithm that reduces communication costs through event-triggered and compressed information exchanges, applicable to directed graphs, with proven convergence and enhanced stochastic mechanisms.

Contribution

It proposes a novel distributed NE seeking algorithm using event-triggered compressed communication over directed graphs, requiring only row-stochastic matrices, and extends it with stochastic mechanisms for improved efficiency.

Findings

Reduces communication costs in distributed NE seeking.

Guarantees linear convergence without sacrificing accuracy.

Demonstrates effectiveness through numerical simulations.

Abstract

Distributed Nash equilibrium (NE) seeking problems for networked games have been widely investigated in recent years. Despite the increasing attention, communication expenditure is becoming a major bottleneck for scaling up distributed approaches within limited communication bandwidth between agents. To reduce communication cost, an efficient distributed NE seeking (ETC-DNES) algorithm is proposed to obtain an NE for games over directed graphs, where the communication efficiency is improved by event-triggered exchanges of compressed information among neighbors. ETC-DNES saves communication costs in both transmitted bits and rounds of communication. Furthermore, our method only requires the row-stochastic property of the adjacency matrix, unlike previous approaches that hinged on doubly-stochastic communication matrices. We provide convergence guarantees for ETC-DNES on games with restricted strongly monotone mappings and testify its efficiency with no sacrifice on the accuracy. The algorithm and analysis are extended to a compressed algorithm with stochastic event-triggered mechanism (SETC-DNES). In SETC-DNES, we introduce a random variable in the triggering condition to further enhance algorithm efficiency. We demonstrate that SETC-DNES guarantees linear convergence to the NE while achieving even greater reductions in communication costs compared to ETC-DNES. Finally, numerical simulations illustrate the effectiveness of the proposed algorithms.