Auctioning Multiple Goods without Priors
Abstract
I consider a mechanism design problem of selling multiple goods to multiple bidders when the designer has minimal amount of information. I assume that the designer only knows the upper bounds of bidders' values for each good and has no additional distributional information. The designer takes a minimax regret approach. The expected regret from a mechanism given a joint distribution over value profiles and an equilibrium is defined as the difference between the full surplus and the expected revenue. The designer seeks a mechanism, referred to as a minimax regret mechanism, that minimizes her worst-case expected regret across all possible joint distributions over value profiles and all equilibria. I find that a separate second-price auction with random reserves is a minimax regret mechanism for general upper bounds. Under this mechanism, the designer holds a separate auction for each good; the formats of these auctions are second-price auctions with random reserves.
Cite
@article{arxiv.2204.13726,
title = {Auctioning Multiple Goods without Priors},
author = {Wanchang Zhang},
journal= {arXiv preprint arXiv:2204.13726},
year = {2022}
}