We show that for any discount factor, there is a natural number M such that all subgame perfect equilibrium outcomes of the discounted repeated prisoners' dilemma can be obtained by subgame perfect equilibrium strategies with the following property: current play depends only on the number of the...

We study the extent to which equilibrium payoffs of discounted repeated games can be obtained by 1 - memory strategies. First, we present robust examples of games in which there is a subgame perfect equilibrium payoff profile that cannot be obtained by any 1 - memory subgame perfect equilibrium....

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 player's repeated game payoff function at each period of time is strictly increasing...