Distributed Nash Equilibrium Seeking for Decomposable Pseudo-Gradient

In this paper, we consider distributed Nash equilibrium seeking in partial-decision information setting. We analyze games that have a pseudo-gradient that can be decomposed into two components, where one component is the gradient of a convex function. Two classes of games that have this decomposition are potential games and cocoercive-related games. We consider standard gradient-play with consensus dynamics and show that they converge in both classes of games in continuous time and discrete time.