  We analyze the robustness of (pure strategy) Nash equilibria for network
games against perturbations of the players' utility functions. We first derive
a simple characterization of the margin of robustness, defined as the minimum
magnitude of a perturbation that makes a Nash equilibrium of the original game
stop being so in the perturbed game. Then, we investigate what the maximally
robust equilibria are in some standard network games such as the coordination
and the anti-coordination game. Finally, as an application, we provide some
sufficient conditions for the existence of Nash equilibria in network games
with a mixture of coordinating and anticoordinating games.
