Localized Perfection

Perfect equilibrium and its refinements are widely studied and typically rely on full-support perturbations. We introduce a S-localized notion of perfection for games with a continuum of players. It confines perturbations within a S-neighborhood of the underlying action distribution and eliminates undesirable equilibria from a local perspective. We establish the existence of a pure strategy S-localized perfect equilibrium and show that it is equivalent to S-admissible Nash equilibrium. We also study limit versions of S-localized perfection. Illustrative applications to large routing games and crowd saturation games are presented.