Unilateral commitment in the finitely repeated prisoners' dilemma

In this paper, we modify the finitely repeated prisoners' dilemma by adding an initial round in which the players have the option of simultaneously, unilaterally and publicly committing themselves, in an enforceable way, to a subset of their strategies. We show that when a large enough number of repetitions of the prisoners' dilemma follow this initial commitment round, then not only do the players have incentives to commit themselves to a limited strategy set, but there is also a symmetric subgame perfect equilibrium in which both players act cooperatively throughout the post-commitment stages of the game.