  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.
