Robust Revenue Maximization Under Minimal Statistical Information

Giannakopoulos Y, Poças D, Tsigonias-Dimitriadis A (2020)

Publication Type: Conference contribution, Original article

Publication year: 2020

Journal

Lecture Notes in Computer Science Springer Verlag

Publisher: Springer Science and Business Media Deutschland GmbH

Book Volume: 12495 LNCS

Pages Range: 177-190

Conference Proceedings Title: Proceedings of the 16th Conference on Web and Internet Economics (WINE)

Event location: Beijing CN

ISBN: 9783030649456

DOI: 10.1007/978-3-030-64946-3_13

Open Access Link: https://arxiv.org/abs/1907.04220

Abstract

We study the problem of multi-dimensional revenue maximization when selling m items to a buyer that has additive valuations for them, drawn from a (possibly correlated) prior distribution. Unlike traditional Bayesian auction design, we assume that the seller has a very restricted knowledge of this prior: they only know the mean μj and an upper bound σj on the standard deviation of each item’s marginal distribution. Our goal is to design mechanisms that achieve good revenue against an ideal optimal auction that has full knowledge of the distribution in advance. Informally, our main contribution is a tight quantification of the interplay between the dispersity of the priors and the aforementioned robust approximation ratio. Furthermore, this can be achieved by very simple selling mechanisms. More precisely, we show that selling the items via separate price lotteries achieves an O(log r) approximation ratio where r= maxj(σj/ μj) is the maximum coefficient of variation across the items. If forced to restrict ourselves to deterministic mechanisms, this guarantee degrades to O(r2). Assuming independence of the item valuations, these ratios can be further improved by pricing the full bundle. For the case of identical means and variances, in particular, we get a guarantee of O(log (r/ m) ) which converges to optimality as the number of items grows large. We demonstrate the optimality of the above mechanisms by providing matching lower bounds. Our tight analysis for the deterministic case resolves an open gap from the work of Azar and Micali [ITCS’13].

Authors with CRIS profile

Ioannis Giannakopoulos

Involved external institutions

University of Lisbon / Universidade de Lisboa (ULisboa) PT Portugal (PT) Technische Universität München (TUM) DE Germany (DE)

How to cite

APA:

Giannakopoulos, Y., Poças, D., & Tsigonias-Dimitriadis, A. (2020). Robust Revenue Maximization Under Minimal Statistical Information. In Xujin Chen, Nikolai Gravin, Martin Hoefer, Ruta Mehta (Eds.), Proceedings of the 16th Conference on Web and Internet Economics (WINE) (pp. 177-190). Beijing, CN: Springer Science and Business Media Deutschland GmbH.

MLA:

Giannakopoulos, Yiannis, Diogo Poças, and Alexandros Tsigonias-Dimitriadis. "Robust Revenue Maximization Under Minimal Statistical Information." Proceedings of the 16th International Conference on Web and Internet Economics, WINE 2020, Beijing Ed. Xujin Chen, Nikolai Gravin, Martin Hoefer, Ruta Mehta, Springer Science and Business Media Deutschland GmbH, 2020. 177-190.

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