Beckmann's approach to multi-item multi-bidder auctions
Theoretical Economics
2022-09-08 v2 Computer Science and Game Theory
Functional Analysis
Optimization and Control
Abstract
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).
Cite
@article{arxiv.2203.06837,
title = {Beckmann's approach to multi-item multi-bidder auctions},
author = {Alexander V. Kolesnikov and Fedor Sandomirskiy and Aleh Tsyvinski and Alexander P. Zimin},
journal= {arXiv preprint arXiv:2203.06837},
year = {2022}
}