An Example of a Repeated Partnership Game with Discounted and with Uniformly Inefficient Equilibria

In this note we present an example of a repeated partnership game with imperfect monitoring in which all supergame equilibria with positive discount rates are bounded away from full efficiency uniformly in the discount rate, provided the latter is strictly positive. On the other hand, if the players do not discount the future, then every efficient one-period payoff vector that dominates the one-period equilibrium payoff vector can be attained by an equilibrium of the repeated game. Thus the correspondence that maps the players' discount rate into the corresponding set of repeated-games equilibrium payoff vectors is discounted at the point at which the discount rate is zero.