Information compression techniques are majorly employed to address the concern of reducing communication cost over peer-to-peer links. In this paper, we investigate distributed Nash equilibrium (NE) seeking problems in a class of non-cooperative games over directed graphs with information compression. To improve communication efficiency, a compressed distributed NE seeking (C-DNES) algorithm is proposed to obtain a NE for games, where the differences between decision vectors and their estimates are compressed. The proposed algorithm is compatible with a general class of compression operators, including both unbiased and biased compressors. Moreover, our approach only requires the adjacency matrix of the directed graph to be row-stochastic, in contrast to past works that relied on balancedness or specific global network parameters. It is shown that C-DNES not only inherits the advantages of conventional distributed NE algorithms, achieving linear convergence rate for games with restricted strongly monotone mappings, but also saves communication costs in terms of transmitted bits. Finally, numerical simulations illustrate the advantages of C-DNES in saving communication cost by an order of magnitude under different compressors.

翻译：信息压缩技术主要用于减少点对点链路中的通信开销。本文研究一类基于有向图且含信息压缩的非合作博弈中的分布式纳什均衡求解问题。为提升通信效率，提出一种压缩分布式纳什均衡求解（C-DNES）算法，该算法通过压缩决策向量与其估计值之间的差异来获取博弈的纳什均衡。所提算法兼容包括无偏与有偏压缩器在内的通用压缩算子类别。此外，与依赖平衡性或特定全局网络参数的既有工作不同，本方法仅需有向图的邻接矩阵满足行随机性即可。理论分析表明，C-DNES不仅继承了传统分布式纳什均衡算法的优势——对具有受限强单调映射的博弈实现线性收敛速率，还能在传输比特数层面节省通信成本。最后，数值仿真验证了在不同压缩器下C-DNES可将通信成本降低一个数量级的优势。