Prior-free Dynamic Mechanism Design With Limited Liability
Abstract
We study the problem of repeatedly auctioning off an item to one of bidders where: a) bidders have a per-round individual rationality constraint, b) bidders may leave the mechanism at any point, and c) the bidders' valuations are adversarially chosen (the prior-free setting). Without these constraints, the auctioneer can run a second-price auction to "sell the business" and receive the second highest total value for the entire stream of items. We show that under these constraints, the auctioneer can attain a constant fraction of the "sell the business" benchmark, but no more than of this benchmark. In the course of doing so, we design mechanisms for a single bidder problem of independent interest: how should you repeatedly sell an item to a (per-round IR) buyer with adversarial valuations if you know their total value over all rounds is but not how their value changes over time? We demonstrate a mechanism that achieves revenue and show that this is tight.
Cite
@article{arxiv.2103.01868,
title = {Prior-free Dynamic Mechanism Design With Limited Liability},
author = {Mark Braverman and Jon Schneider and S. Matthew Weinberg},
journal= {arXiv preprint arXiv:2103.01868},
year = {2021}
}