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Envy-Free Pricing in Large Markets: Approximating Revenue and Welfare

Authors:

Elliot Anshelevich,

Shreyas SekarAuthors Info & Claims

ACM Transactions on Economics and Computation (TEAC), Volume 5, Issue 3

Article No.: 16, Pages 1 - 42

https://doi.org/10.1145/3105786

Published: 09 August 2017 Publication History

Abstract

We study the classic setting of envy-free pricing, in which a single seller chooses prices for its many items, with the goal of maximizing revenue once the items are allocated. Despite the large body of work addressing such settings, most versions of this problem have resisted good approximation factors for maximizing revenue; this is true even for the classic unit-demand case. In this article, we study envy-free pricing with unit-demand buyers, but unlike previous work we focus on large markets: ones in which the demand of each buyer is infinitesimally small compared to the size of the overall market. We assume that the buyer valuations for the items they desire have a nice (although reasonable) structure, that is, that the aggregate buyer demand has a monotone hazard rate and that the values of every buyer type come from the same support.

For such large markets, our main contribution is a 1.88-approximation algorithm for maximizing revenue, showing that good pricing schemes can be computed when the number of buyers is large. We also give a (e,2)-bicriteria algorithm that simultaneously approximates both maximum revenue and welfare, thus showing that it is possible to obtain both good revenue and welfare at the same time. We further generalize our results by relaxing some of our assumptions and quantify the necessary tradeoffs between revenue and welfare in our setting. Our results are the first known approximations for large markets and crucially rely on new lower bounds, which we prove for the revenue-maximizing prices.

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Cited By

Salvatierra MSalvatierra MColonna J(2021)Short Communication: Optimally Solving the Unit-Demand Envy-Free Pricing Problem with Metric Substitutability in Cubic TimeAlgorithms10.3390/a1410027914:10(279)Online publication date: 26-Sep-2021
https://doi.org/10.3390/a14100279
Flammini MMauro MTonelli M(2020)On Fair Price Discrimination in Multi-Unit MarketsArtificial Intelligence10.1016/j.artint.2020.103388(103388)Online publication date: Sep-2020
https://doi.org/10.1016/j.artint.2020.103388
Markakis ENtokos ATelelis O(2020)On Envy-Free Revenue Approximation for Combinatorial Buyers with BudgetsTheory of Computing Systems10.1007/s00224-020-09984-764:8(1338-1361)Online publication date: 9-Jun-2020
https://dl.acm.org/doi/10.1007/s00224-020-09984-7
Show More Cited By

Index Terms

Envy-Free Pricing in Large Markets: Approximating Revenue and Welfare
1. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
  2. Theory and algorithms for application domains
    1. Algorithmic game theory and mechanism design
      1. 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 3

August 2017

107 pages

ISSN:2167-8375

EISSN:2167-8383

DOI:10.1145/3129279

Editors:
David Pennock
Microsoft
,
Ilya Segal
Stanford University

Issue’s Table of Contents

Copyright © 2017 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 09 August 2017

Accepted: 01 March 2017

Revised: 01 February 2017

Received: 01 October 2016

Published in TEAC Volume 5, Issue 3

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Cited By

Salvatierra MSalvatierra MColonna J(2021)Short Communication: Optimally Solving the Unit-Demand Envy-Free Pricing Problem with Metric Substitutability in Cubic TimeAlgorithms10.3390/a1410027914:10(279)Online publication date: 26-Sep-2021
https://doi.org/10.3390/a14100279
Flammini MMauro MTonelli M(2020)On Fair Price Discrimination in Multi-Unit MarketsArtificial Intelligence10.1016/j.artint.2020.103388(103388)Online publication date: Sep-2020
https://doi.org/10.1016/j.artint.2020.103388
Markakis ENtokos ATelelis O(2020)On Envy-Free Revenue Approximation for Combinatorial Buyers with BudgetsTheory of Computing Systems10.1007/s00224-020-09984-764:8(1338-1361)Online publication date: 9-Jun-2020
https://dl.acm.org/doi/10.1007/s00224-020-09984-7
Flammini MMauro MTonelli M(2018)On fair price discrimination in multi-unit marketsProceedings of the 27th International Joint Conference on Artificial Intelligence10.5555/3304415.3304451(247-253)Online publication date: 13-Jul-2018
https://dl.acm.org/doi/10.5555/3304415.3304451

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