Abstract
We compare the properties of several notions of trembling-hand perfection within classes of compact, metric, and possibly discontinuous games, and show that in the presence of payoff discontinuities, standard notions of trembling-hand perfection fail a weakening of admissibility termed limit admissibility. We also provide conditions ensuring the existence of a limit admissible perfect equilibrium.
► Some properties of perfect equilibria in discontinuous games are studied. ► Standard notions of perfection fail limit admissibility. ► The notion of limit admissible perfection is introduced. ► Limit admissible perfect equilibria exist in discontinuous games.