Optimal selling mechanisms with countervailing positive externalities and an application to tradable retaliation in the WTO

We study revenue-maximizing mechanisms for a seller who sells an indivisible good to several buyers with positive, type-dependent and countervailing allocative externalities. To cope with the difficulty of types obtaining reservation utilities being endogenously determined, we first solve a minimax version of the seller's problem by generalizing Myerson's characterization techniques for the non-regular case. The solution is then shown to solve the seller's original maximin problem as well in our setting. We find that the seller's optimal mechanism normally features bunching even in the regular case and the type with the lowest expected payoff is typically not an extreme type. As an important illustration of our characterization procedures, we apply our results to the problem of selling retaliation rights in the WTO.