  We consider the problem of revenue-maximizing Bayesian auction design with
several bidders having independent private values over several items. We show
that it can be reduced to the problem of continuous optimal transportation
introduced by Beckmann (1952) where the optimal transportation flow generalizes
the concept of ironed virtual valuations to the multi-item setting. We
establish the strong duality between the two problems and the existence of
solutions. The results rely on insights from majorization and optimal
transportation theories and on the characterization of feasible interim
mechanisms by Hart and Reny (2015).
