I analyze the set of pure strategy subgame perfect Nash equilibria of any

finitely repeated game with complete information and perfect monitoring. The main

result is a complete characterization of the limit set, as the time horizon increases, of

the set of pure strategy subgame perfect Nash equilibrium payoff vectors of the finitely

repeated game. The same method can be used to fully characterize the limit set of the

set of pure strategy Nash equilibrium payoff vectors of any the finitely repeated game.