On Voluntary and Repeatable Partnerships under No Information Flow

We investigate the range of payoffs which are achieved by voluntary and repeatable partnerships under no information flow. In each period, players without a partner are randomly matched and have an option to form a partnership on meeting a new opponent. A partnership forms and continues only by mutual agreement. Actions are observed only by partners and a player starts with a null history once a partnership terminates. We show that any payoff vector that is feasible and Pareto dominates the payoff vector without a partner is sustainable under sufficiently low probabilities to form a new partnership. Therefore the options to form and to terminate a partnership help the players achieve non-myopic equilibria, even though personalized punishments are impossible. The equilibrium payoff sequences display a generalized “starting small” property. An extension to n population is straightforward and adding preplay negotiations still leads to a folk theorem.