On Optimal Social Convention in Voluntary Continuation Prisoner's Dilemma Games

When the repeated prisoner's dilemma setup is generalized to allow for a unilateral breakup, maximal efficiency in equilibrium remains an open question. With restrictions of simple symmetry with eternal mutual cooperation, defection, or (matched) alternation on the equilibrium path, we describe the upper limit of discounted lifetime payoff and construct simple social conventions that, for a large set of parameters, achieve it. While all other well-known equilibrium designs in the literature punish defections with a breakup and thus reach the optimum only in degenerate cases, exploited cooperators in ours allow defectors to compensate them by cooperating more in the future.