On the Optimal Degree of Cooperation in the Repeated Prisoner's Dilemma with Side Payments

We analyze how agents use side payments to induce cooperation in the infinitely repeated Prisoners' Dilemma. We characterize the Pareto frontier of the set of subgame perfect equilibrium payoffs for all possible combinations of discount factors. Play paths implementing Pareto dominant equilibrium payoffs are uniquely determined in all but the first period. Full cooperation, supported by repeated payments from the patient player to the impatient, does not necessarily implement such payoffs, even when such behavior maximizes total stage game payoffs. Rather, when the difference in players' discount factors is sufficiently large, all Pareto dominant equilibrium payoffs are implemented by partial cooperation supported by repeated payments from the impatient player to the patient. When both players are sufficiently patient, such payoffs, while implemented via full cooperation, are in fact supported by repeated payments from the impatient player to the patient. We characterize conditions under which public randomization has no impact on the Pareto frontier and also, conditions under which our Pareto dominant equilibrium payoffs are robust to renegotiation-proofness.