Linear Convergent Distributed Nash Equilibrium Seeking with Compression

Information compression techniques are often employed to reduce 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 multi-agent networks with information compression. To improve system scalability and communication efficiency, a compressed distributed NE seeking (C-DNES) algorithm is proposed to obtain a Nash equilibrium 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. It is shown that C-DNES not only inherits the advantages of the conventional distributed NE algorithms, achieving linear convergence rate for games with strongly monotone mappings, but also saves communication costs in terms of transmitted bits. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed algorithm.