Invasion dynamics of the finitely repeated Prisoner's Dilemma game

Computer simulations have shown that mutation-selection processes frequently lead to the establishment of cooperation in the repeated prisoner's dilemma. To simplify the mathematical analysis, it has usually been assumed that the interaction is repeated infinitely often. Here, we consider the finitely repeated case. Using renewal equations, we derive analytic results on the adaptive dynamics of monomorphic populations evolving in trait-space, describe the cooperation-rewarding zone and specify when unconditional defectors can invade. Tit for tat plays an essential, but transient, role in the evolution of cooperation. A large part of the paper considers the case when players make their moves not simultaneously, but alternatingly