Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Braun, Alexander; Buttkus, Matthias; Kesselheim, Thomas https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-146038
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Asymptotically Optimal Welfare of Posted Pricing for Multiple Items with MHR Distributions

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Abstract

We consider the problem of posting prices for unit-demand buyers if all n buyers have identically distributed valuations drawn from a distribution with monotone hazard rate. We show that even with multiple items asymptotically optimal welfare can be guaranteed.
Our main results apply to the case that either a buyer’s value for different items are independent or that they are perfectly correlated. We give mechanisms using dynamic prices that obtain a 1 - Θ (1/(log n))-fraction of the optimal social welfare in expectation. Furthermore, we devise mechanisms that only use static item prices and are 1 - Θ ((log log log n)/(log n))-competitive compared to the optimal social welfare. As we show, both guarantees are asymptotically optimal, even for a single item and exponential distributions.

BibTeX - Entry

@InProceedings{braun_et_al:LIPIcs.ESA.2021.22,
  author =	{Braun, Alexander and Buttkus, Matthias and Kesselheim, Thomas},
  title =	{{Asymptotically Optimal Welfare of Posted Pricing for Multiple Items with MHR Distributions}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{22:1--22:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14603},
  URN =		{urn:nbn:de:0030-drops-146038},
  doi =		{10.4230/LIPIcs.ESA.2021.22},
  annote =	{Keywords: Prophet Inequalities, Monotone Hazard Rate, Competitive Analysis, Posted Prices, Combinatorial Auctions, Matching}
}

Keywords: Prophet Inequalities, Monotone Hazard Rate, Competitive Analysis, Posted Prices, Combinatorial Auctions, Matching
Seminar: 29th Annual European Symposium on Algorithms (ESA 2021)
Issue date: 2021
Date of publication: 31.08.2021


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