  In this paper, we consider game problems played by (multi)-integrator agents,
subject to external disturbances. We propose Nash equilibrium seeking dynamics
based on gradient-play, augmented with a dynamic internal-model based
component, which is a reduced-order observer of the disturbance. We consider
single-, double- and extensions to multi-integrator agents, in a
partial-information setting, where agents have only partial knowledge on the
others' decisions over a network. The lack of global information is offset by
each agent maintaining an estimate of the others' states, based on local
communication with its neighbours. Each agent has an additional dynamic
component that drives its estimates to the consensus subspace. In all cases, we
show convergence to the Nash equilibrium irrespective of disturbances. Our
proofs leverage input-to-state stability under strong monotonicity of the
pseudo-gradient and Lipschitz continuity of the extended pseudo-gradient.
