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We consider stability of equilibria for population games against slight perturbation on the social state space. We provide a necessary and sufficient condition for the existence of Nash equilibria for perturbed population games, which is very important and interesting. Then, refinements of equilibria for population games are introduced. Equivalent characterizations of perfect equilibrium are given. At last, it is shown that each population game admits at least one perfect (proper, weakly proper, and robust) equilibrium.

Refinements of Equilibria for Population Games Based on Bounded Rationality of Agents