The probability to receive the first item as a function of bidder’s values $(x_1, x_2)$in the optimal 2-bidder 2-item auction with i.i.d. values uniform on $[0, 1]$.
Abstract
We consider the problem of revenue-maximizing Bayesian auction design with several i.i.d. bidders and several items. We show that the auction- design problem can be reduced to the problem of continuous optimal trans- portation 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-to- single-agent reduction and the majorization theory insights to characterize the solution.
Type
Publication
In arXiv