  In this paper, 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, that we call "Heavy Anchor". We prove that Heavy Anchor
allows a relaxation of strict monotonicity of the pseudo-gradient, 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. Each player maintains a
local decision variable and an auxiliary state estimate and communicates with
their neighbours to learn the opponents' actions. We modify Heavy Anchor via a
distributed Laplacian feedback and show how we can exploit
equilibrium-independent passivity properties to achieve convergence to a Nash
equilibrium in hypomonotone regimes.
