Beckmann’s Approach to Multi-item Multi-bidder Auctions

We consider the problem of revenue-maximizing Bayesian auction design with several i.i.d. bidders and several items. We show that the auctiondesign problem can be reduced to the problem of continuous optimal transportation introduced by Beckmann (1952). We establish the strong duality between the two problems and demonstrate the existence of solutions. We then develop a new numerical approximation scheme that combines multi-tosingle-agent reduction and the majorization theory insights to characterize the solution.