Geometric Convergence of Gradient Play Algorithms for Distributed Nash Equilibrium Seeking

We study distributed algorithms for seeking a Nash equilibrium in class of convex networked games with strongly monotone mappings. Each player has access to her own smooth local cost function and can communicate neighbors some undirected graph. To deal fast learning equilibria under such settings, we introduce so called augmented game mapping provide conditions which this is monotone. consider gradient play algorithm determining (GRANE). The involves every performing step minimize while sharing retrieving information locally among the network. Using reformulation problem based on strong mapping, prove convergence geometric rate. Furthermore, Nesterov type acceleration algorithm. demonstrate that, similarly accelerated centralized optimization variational inequality problems, our outperforms GRANE Moreover, relax assumptions required guarantee analyze restricted property milder assumptions.