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Asymptotically Optimal Welfare of Posted Pricing for Multiple Items with MHR Distributions

Authors: Alexander Braun, Matthias Buttkus, and Thomas Kesselheim

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)


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.

Cite as

Alexander Braun, Matthias Buttkus, and Thomas Kesselheim. Asymptotically Optimal Welfare of Posted Pricing for Multiple Items with MHR Distributions. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@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/entities/document/10.4230/LIPIcs.ESA.2021.22},
  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}
}
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