Forever and a Day

Abstract

The focus of this chapter is on the Iterated Prisoners’ Dilemma and Robert Axelrod’s “Tournament of Strategies.” If a Prisoners’ Dilemma is repeated and the repetitions are with “unforeseeable end,” then an equilibrium exists that implies “cooperation” in every round of the supergame. This result is the most prominent implication of the Folk Theorem formalizing “what we have always known.” An obvious condition of achieving this “favorable result” is that the players appreciate future benefits and do not discount them too heavily. Another condition is that players know that this also applies to their opponents. In Axelrod’s tournament, strategies are randomly matched in pairs. The strategies prescribe the decision in each period for a finite number of periods. For instance, the winning strategy, i.e., TIT-FOR TAT, proposes that the player “cooperates” in the first period and repeats this choice in the following periods as long as the strategy of the opponent chooses “cooperate.” However, if the strategy selects “defect,” then TIT-FOR TAT presents “defect” as well. The strategy resulting in the largest sum of payoff points wins. This condition is different than what defines success in the Iterated Prisoners’ Dilemma.