Improved Revenue Bounds for Posted-Price and Second-Price Mechanisms

47 Pages Posted: 12 Aug 2020

See all articles by Hedyeh Beyhaghi

Hedyeh Beyhaghi

Cornell University

Negin Golrezaei

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Renato Paes Leme

Google Inc.

Martin Pál

Google

Balasubramanian Sivan

Google Inc., New York

Date Written: July 15, 2020

Abstract

We study revenue maximization through sequential posted-price (SPP) mechanisms in single-dimensional settings with n buyers and independent but not necessarily identical value distributions. We construct the SPP mechanisms by considering the best of two simple pricing rules: one that imitates the optimal/Myersonian mechanism via the taxation principle and the other that posts a uniform price. Our pricing rules are rather generalizable and yield the first improvement over long-established approximation factors in several settings. We design factor-revealing mathematical programs that crisply capture the approximation factor of our SPP mechanism. In the single-unit setting, our SPP mechanism yields a better approximation factor than the state of the art prior to our work (Azar et al. 2018). In the multi-unit setting, our SPP mechanism yields the first improved approximation factor over the state of the art after over nine years (Yan (2011) and Chakraborty et al. (2010)). Our results on SPP mechanisms immediately imply improved performance guarantees for the equivalent free-order prophet inequality problem. In the position auction setting, our SPP mechanism yields the first higher-than 1 − 1/e approximation factor. In eager second-price (ESP) auctions, our two simple pricing rules lead to the first improved approximation factor that is strictly greater than what is obtained by the SPP mechanism in the single-unit setting

Keywords: posted-price mechanisms, eager second-price auctions, multi-unit, position auctions, online advertising

Suggested Citation

Beyhaghi, Hedyeh and Golrezaei, Negin and Paes Leme, Renato and Pál, Martin and Sivan, Balasubramanian, Improved Revenue Bounds for Posted-Price and Second-Price Mechanisms (July 15, 2020). Available at SSRN: https://ssrn.com/abstract=3652081 or http://dx.doi.org/10.2139/ssrn.3652081

Hedyeh Beyhaghi

Cornell University ( email )

Ithaca, NY 14853
United States

Negin Golrezaei (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

100 Main Street
E62-416
Cambridge, MA 02142
United States
02141 (Fax)

Renato Paes Leme

Google Inc. ( email )

1600 Amphitheatre Parkway
Second Floor
Mountain View, CA 94043
United States

Martin Pál

Google ( email )

1600 Amphitheatre Parkway
Second Floor
Mountain View, CA 94043
United States

Balasubramanian Sivan

Google Inc., New York ( email )

111 8th Ave
New York, NY 10011
United States

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