O'Neill's Theorem for Games

This presentation is a mix of two papers: O'Neill's Theorem for PL-Approximations (joint with S. Govindan) and O'Neill's Theorem for Games (joint with S. Govindan and R. Laraki). O'Neill's Theorem in fixed point theory (B. O'Neill, 1953) presents the structure of fixed points of a map around a connected component of fixed points under perturbations of the map. We prove a game-theoretic version of this theorem which shows the structure of Nash-equilibria around a component of Nash-equilibria under payoff perturbations.