BOUNDED COMPLEXIIT JUSTIFIES COOPERATION IN THE FINITELY REPEATED PRISONERS ' DILEMMA

Cooperation in the finitely repeated prisoner's dilemma is justified, without departure from strict utility maximization or complete information, but under the assumption that there are bounds (possibly very large) to the complexity of the strategies that the players may use. It has often been observed that cooperative behavior may emerge in non-cooperative situations when the nature of the interactions is long term. A fundamental message of the theory of repeated games is that the cooperative outcomes of multiperson games, provided those games are repeated over and over, are consistent with the usual 'selfish ' utility-maximizing behavior assumed in economic theory. This message is delivered through the Folk theorem and several other results [Aumann (1959,1960,1981). Aumann and Shapley (1976), Rubinstein (1979,1980), Smale (1980) and Sorin (1983)], which assert that cooperative outcomes of the one-shot game are Nash equilibria (and also perfect equilibria) of the infinite repetition of that game. In some cases, the Nash equilibria of finitely repeated games also rationalize cooperation; this happens when the convex hull of the (vector) equilibrium payoffs contains a point that strictly dominates the smallest individually rational payoffs [Benoit and Krishna (1984)]. However, the prisoners ' dilemma is not in this class of games; indeed, in any finite repetition of this game, all equilibria lead to the non-cooperative outcome at each stage