The value of linking: Efficiency and public punishment

Jimmy Chan | Fudan University

We consider repeated games with mediation and side-payments. We show that any punishment scheme can be divided into a public part and a private part. While private punishment can be reduced by linking, public punishment must be carried out in equilibrium. The total average equilibrium payoff is bounded from above by the payoff from enforcing the correlated action profile with the highest total stage-game payoff net of public punishment. The bound is tight. For any epsilon there exists an equilibrium with total average payoff epsilon close to the upper bound when the players are sufficiently patient. Our results extend the insights of Abreu, Milgrom, and Pearce (1991) and incorporate a number of existing results in the literature.