Before revision: This paper introduces three notions of perfect equilibriumfor 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 .
After revision: This paper introduces three notions of perfect equilibriumfor games with many players . Such an equilibrium is shown to exist and satisfy the important behavioral principles of admissibility, trembling-hand perfection, and ex post perfection. These robustness properties strengthen relevant equilibrium results in the large literature on strategic interactions of many agents. Illustrative applications to congestion games and potential games are presented. In the particular case of a congestion game with strictly increasing cost functions, we show that there is a unique equilibrium traffic flow induced by robust perfect equilibria .