An Efficient Distributed Nash Equilibrium Seeking With Compressed and Event-Triggered Communication

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 event-triggered and compressed distributed NE seeking (ETC-DNES) algorithm is proposed in this article 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, i.e., stochastic event-triggered and compressed distributed NE seeking (SETC-DNES) algorithm. In SETC-DNES, we introduce a random variable in the triggering condition to further enhance the 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.