Equilibrium Outcomes of Repeated Two-Person Zero-Sum Games∗

We consider discounted repeated two-person zero-sum games. We show that even when players have different discount factors (in which case the repeated game is not a zero-sum game), an outcome is subgame perfect if and only if all of its components are Nash equilibria of the stage game. This implies that in all subgame perfect equilibria, each player’s payoff is equal to his minmax payoff. In conclusion, the competitive nature of two-player zero-sum games is not altered when the game is repeated