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Applications of α-Strongly Regular Distributions to Bayesian Auctions

Authors:

Shravas RaoAuthors Info & Claims

ACM Transactions on Economics and Computation (TEAC), Volume 5, Issue 4

Article No.: 18, Pages 1 - 29

https://doi.org/10.1145/3157083

Published: 22 December 2017 Publication History

Abstract

Two classes of distributions that are widely used in the analysis of Bayesian auctions are the monotone hazard rate (MHR) and regular distributions. They can both be characterized in terms of the rate of change of the associated virtual value functions: for MHR distributions, the condition is that for values v < v^′, ϕ (v^′) - ϕ (v) ≥ v^′ - v, and for regular distributions, ϕ (v^′) - ϕ (v) ≥ 0. Cole and Roughgarden introduced the interpolating class of α-strongly regular distributions (α-SR distributions for short), for which ϕ (v^′) - ϕ (v) ≥ α (v^′ - v), for 0 ≤ α ≤ 1.

In this article, we investigate five distinct auction settings for which good expected revenue bounds are known when the bidders’ valuations are given by MHR distributions. In every case, we show that these bounds degrade gracefully when extended to α-SR distributions. For four of these settings, the auction mechanism requires knowledge of these distributions (in the remaining setting, the distributions are needed only to ensure good bounds on the expected revenue). In these cases, we also investigate what happens when the distributions are known only approximately via samples, specifically how to modify the mechanisms so that they remain effective and how the expected revenue depends on the number of samples.

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Cited By

Giannakopoulos YPoças DTsigonias-Dimitriadis A(2022)Robust Revenue Maximization Under Minimal Statistical InformationACM Transactions on Economics and Computation10.1145/354660610:3(1-34)Online publication date: 2-Sep-2022
https://dl.acm.org/doi/10.1145/3546606
Giannakopoulos YPoças DZhu K(2021)Optimal Pricing for MHR and λ-regular DistributionsACM Transactions on Economics and Computation10.1145/34344239:1(1-28)Online publication date: 2-Jan-2021
https://dl.acm.org/doi/10.1145/3434423
Schweizer NSzech N(2019)Performance bounds for optimal sales mechanisms beyond the monotone hazard rate conditionJournal of Mathematical Economics10.1016/j.jmateco.2019.02.007Online publication date: Mar-2019
https://doi.org/10.1016/j.jmateco.2019.02.007

Index Terms

Applications of α-Strongly Regular Distributions to Bayesian Auctions
1. Theory of computation
  1. Theory and algorithms for application domains
    1. Algorithmic game theory and mechanism design
      1. Algorithmic mechanism design
      2. Computational pricing and auctions

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Published In

cover image ACM Transactions on Economics and Computation

ACM Transactions on Economics and Computation Volume 5, Issue 4

Special Issue on Wine'15

November 2017

146 pages

ISSN:2167-8375

EISSN:2167-8383

DOI:10.1145/3174276

Editors:
David Pennock
Microsoft
,
Ilya Segal
Stanford University

Issue’s Table of Contents

Copyright © 2017 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 22 December 2017

Accepted: 01 July 2017

Revised: 01 January 2017

Received: 01 July 2016

Published in TEAC Volume 5, Issue 4

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Cited By

Giannakopoulos YPoças DTsigonias-Dimitriadis A(2022)Robust Revenue Maximization Under Minimal Statistical InformationACM Transactions on Economics and Computation10.1145/354660610:3(1-34)Online publication date: 2-Sep-2022
https://dl.acm.org/doi/10.1145/3546606
Giannakopoulos YPoças DZhu K(2021)Optimal Pricing for MHR and λ-regular DistributionsACM Transactions on Economics and Computation10.1145/34344239:1(1-28)Online publication date: 2-Jan-2021
https://dl.acm.org/doi/10.1145/3434423
Schweizer NSzech N(2019)Performance bounds for optimal sales mechanisms beyond the monotone hazard rate conditionJournal of Mathematical Economics10.1016/j.jmateco.2019.02.007Online publication date: Mar-2019
https://doi.org/10.1016/j.jmateco.2019.02.007
Cui THamilton M(undefined)Optimal Feature-Based Market Segmentation and PricingSSRN Electronic Journal10.2139/ssrn.4151103
https://doi.org/10.2139/ssrn.4151103

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