On the Exact Convergence to Nash Equilibrium in Hypomonotone Regimes Under Full and Partial-Decision Information
Dian Gadjov, Lacra Pavel
Abstract
In this article, we consider distributed Nash equilibrium seeking in monotone and hypomonotone games. We first assume that each player has knowledge of the opponents’ decisions and propose a passivity-based modification of the standard gradient-play dynamics, which we call “Heavy Anchor.” We prove that Heavy Anchor allows a relaxation of strict monotonicity of the pseudogradient, needed for gradient-play dynamics, and can ensure exact asymptotic convergence in merely monotone regimes. We extend these results to the setting where each player has only partial information of the opponents’ decisions. In addition, by introducing an inverse Lipschitz property, we are able to extend the results to hypomonotone games. We modify Heavy Anchor via a distributed Laplacian feedback and show how we can exploit equilibrium-independent passivity properties to achieve convergence to the Nash equilibrium in hypomonotone regimes.