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In this paper, we consider distributed Nash equilibrium seeking in monotoneand hypomonotone games. We first assume that each player has knowledge of theopponents' decisions and propose a passivity-based modification of the standardgradient-play dynamics, that we call "Heavy Anchor". We prove that Heavy Anchorallows a relaxation of strict monotonicity of the pseudo-gradient, needed forgradient-play dynamics, and can ensure exact asymptotic convergence in merelymonotone regimes. We extend these results to the setting where each player hasonly partial information of the opponents' decisions. Each player maintains alocal decision variable and an auxiliary state estimate and communicates withtheir neighbours to learn the opponents' actions. We modify Heavy Anchor via adistributed Laplacian feedback and show how we can exploitequilibrium-independent passivity properties to achieve convergence to a Nashequilibrium in hypomonotone regimes.

On the exact convergence to Nash equilibrium in hypomonotone regimes under full and partial-information