Evolutionary stability in the finitely repeated prisoner's dilemma game

The dynamic evolutionary stability of mutual defection is proven for the repeated prisoner's dilemma game where payoffs are cumulative and the number of repetitions is known. This agrees with the classical result that the only Nash equilibrium outcome is to defect al all stages of this repeated game. Moreover, it is shown that, for any initial polymorphic population, the evolutionary dynamic converges to a unique Nash equilibrium strategy that depends on the original polymorphism. Both these results confirm earlier conjectures concerning the application of evolutionary game theory to the repeated prisoner's dilemma. (C) 1996 Academic Press, Inc.