Equilibrium refinements in games with many players.

This paper introduces three notions of perfect equilibrium for games with many players, respectively, in behavioral, mixed and pure strategies. The equivalence between behavioral strategy perfect equilibrium and mixed strategy perfect equilibrium is established. More importantly, it is shown that after the resolution of strategic uncertainty, a mixed strategy perfect equilibrium leads to a pure strategy perfect equilibrium almost surely. Various properties related to limit admissibility are also considered.