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Distributed Nash equilibrium (NE) seeking problems for networked games havebeen widely investigated in recent years. Despite the increasing attention,communication expenditure is becoming a major bottleneck for scaling updistributed 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 thecommunication efficiency is improved by event-triggered exchanges of compressedinformation among neighbors. ETC-DNES saves communication costs in bothtransmitted bits and rounds of communication. Furthermore, our method onlyrequires the row-stochastic property of the adjacency matrix, unlike previousapproaches that hinged on doubly-stochastic communication matrices. We provideconvergence guarantees for ETC-DNES on games with restricted strongly monotonemappings and testify its efficiency with no sacrifice on the accuracy. Thealgorithm and analysis are extended to a compressed algorithm with stochasticevent-triggered mechanism (SETC-DNES). In SETC-DNES, we introduce a randomvariable in the triggering condition to further enhance algorithm efficiency.We demonstrate that SETC-DNES guarantees linear convergence to the NE whileachieving even greater reductions in communication costs compared to ETC-DNES.Finally, numerical simulations illustrate the effectiveness of the proposedalgorithms.

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