Optimal Pricing for MHR and λ-regular Distributions

Giannakopoulos Y, Pocas D, Zhu K (2021)

Publication Type: Journal article

Publication year: 2021

Journal

ACM Transactions on Economics and Computation Association for Computing Machinery (ACM)

Book Volume: 9

Pages Range: 2:1--2:28

Article Number: 3434423

Journal Issue: 1

DOI: 10.1145/3434423

Open Access Link: https://arxiv.org/abs/1810.00800

Abstract

We study the performance of anonymous posted-price selling mechanisms for a standard Bayesian auction setting, where n bidders have i.i.d. valuations for a single item. We show that for the natural class of Monotone Hazard Rate (MHR) distributions, offering the same, take-it-or-leave-it price to all bidders can achieve an (asymptotically) optimal revenue. In particular, the approximation ratio is shown to be 1+O(ln ln n/ ln n), matched by a tight lower bound for the case of exponential distributions. This improves upon the previously best-known upper bound of e/(e-1)≈ 1.58 for the slightly more general class of regular distributions. In the worst case (over n), we still show a global upper bound of 1.35. We give a simple, closed-form description of our prices, which, interestingly enough, relies only on minimal knowledge of the prior distribution, namely, just the expectation of its second-highest order statistic. Furthermore, we extend our techniques to handle the more general class of λ-regular distributions that interpolate between MHR (λ =0) and regular (λ =1). Our anonymous pricing rule now results in an asymptotic approximation ratio that ranges smoothly, with respect to λ, from 1 (MHR distributions) to e/(e-1) (regular distributions). Finally, we explicitly give a class of continuous distributions that provide matching lower bounds, for every λ.

Authors with CRIS profile

Ioannis Giannakopoulos

Involved external institutions

Georgia Institute of Technology US United States (USA) (US) University of Lisbon / Universidade de Lisboa (ULisboa) PT Portugal (PT) Technische Universität München (TUM) DE Germany (DE)

How to cite

APA:

Giannakopoulos, Y., Pocas, D., & Zhu, K. (2021). Optimal Pricing for MHR and λ-regular Distributions. ACM Transactions on Economics and Computation, 9(1), 2:1--2:28. https://dx.doi.org/10.1145/3434423

MLA:

Giannakopoulos, Yiannis, Diogo Pocas, and Keyu Zhu. "Optimal Pricing for MHR and λ-regular Distributions." ACM Transactions on Economics and Computation 9.1 (2021): 2:1--2:28.

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