Essential equilibrium in normal-form games with perturbed actions and payoffs

A Nash equilibrium of a normal-form game G is essential if it is robust to perturbations of G. A game is essential if all of its Nash equilibria are essential. This paper provides conditions on the primitives of a (possibly) discontinuous game that guarantee the generic existence of essential games. Unlike the extant literature, the present analysis allows for perturbations of the players' action spaces, in addition to the standard payoff perturbations.