On the exact convergence to Nash equilibrium in monotone regimes under partial-information

In this paper, we consider distributed Nash equilibrium seeking in (non-strictly/strongly) monotone games. We assume first that each player has full access to the opponents' decisions and propose a new higher-order gradient play dynamics, constructed by a passivity-based modification of a standard scheme. We show that this technique allows relaxation of strict monotonicity of the pseudo-gradient and, unlike other methods, can ensure exact asymptotic convergence in merely monotone regimes. We consider next that players have only partial-decision information, and can communicate with their neighbours over an arbitrary undirected graph. To distribute the problem we augment the variables, so that each player has local decision and auxiliary state estimates. We modify the higher-order gradient dynamics via a distributed Laplacian feedback and show how we can exploit equilibrium-independent passivity properties to achieve convergence to a Nash equilibrium in monotone regimes, under different assumptions on the game map.