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. We then prove existence results for a new “finitistic” infinite-game generalization of Selten’s (Int J Game Theory 4: 25–55, 1975) 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.