Equilibrium Outcomes in Repeated Two-Person, Zero-Sum Games

We will consider repeated two-person, zero-sum games in which the preferences in the repeated game depend on the stage-game references, although not necessarily in a time-consistent way. We will assume that each players repeated game payoff function at each period of time is strictly increasing on the stage game payoffs and that the repeated game is itself a zero-sum game in every period. Under these assumptions, we will show that an outcome is a subgame perfect outcome if and only if its components are all Nash equilibria of the stage game.