Approximation results for discontinuous games with an application to equilibrium refinement

We provide approximation results for Nash equilibria in possibly discontinuous games when payoffs and strategy sets are perturbed, and compare these conditions to those considered in the related literature. We then prove existence results for a new "finitistic" infinite-game generalization of Selten's [17] notion of perfection, and study some of its properties. The existence results, which rely on the approximation theorems, relate existing notions of perfection to the new specification. -- discontinuous game ; Nash equilibrium correspondence ; payoff security ; trembling-hand perfect equilibrium ; limit-of-finite perfect equilibrium