Fully Distributed Nash Equilibrium Seeking Over Time-Varying Communication Networks With Linear Convergence Rate

We design a distributed algorithm for learning Nash equilibria over time-varying communication networks in partial-decision information scenario, where each agent can access its own cost function and local feasible set, but only observe the actions of some neighbors. Our is based on projected pseudo-gradient dynamics, augmented with consensual terms. Under strong monotonicity Lipschitz continuity game mapping, we provide very simple proof linear convergence, contractivity property iterates. Compared to similar solutions proposed literature, also allow derive tighter bounds step sizes that ensure convergence. In fact, our numerical simulations, outperforms existing gradient-based methods, when are set their theoretical upper bounds. Finally, relax assumptions network structure, propose different algorithm, which guaranteed converge balanced directed graphs.