License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2020.39
URN: urn:nbn:de:0030-drops-133833
URL: https://drops.dagstuhl.de/opus/volltexte/2020/13383/
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Bérczi, Kristóf ; Kakimura, Naonori ; Kobayashi, Yusuke

Market Pricing for Matroid Rank Valuations

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Abstract

In this paper, we study the problem of maximizing social welfare in combinatorial markets through pricing schemes. We consider the existence of prices that are capable to achieve optimal social welfare without a central tie-breaking coordinator. In the case of two buyers with matroid rank valuations, we give polynomial-time algorithms that always find such prices when one of the matroids is a simple partition matroid or both matroids are strongly base orderable. This result partially answers a question raised by Düetting and Végh in 2017. We further formalize a weighted variant of the conjecture of Düetting and Végh, and show that the weighted variant can be reduced to the unweighted one based on the weight-splitting theorem for weighted matroid intersection by Frank. We also show that a similar reduction technique works for M^♮-concave functions, or equivalently, for gross substitutes functions.

BibTeX - Entry

@InProceedings{brczi_et_al:LIPIcs:2020:13383,
  author =	{Krist{\'o}f B{\'e}rczi and Naonori Kakimura and Yusuke Kobayashi},
  title =	{{Market Pricing for Matroid Rank Valuations}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{39:1--39:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Yixin Cao and Siu-Wing Cheng and Minming Li},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13383},
  URN =		{urn:nbn:de:0030-drops-133833},
  doi =		{10.4230/LIPIcs.ISAAC.2020.39},
  annote =	{Keywords: Pricing schemes, Walrasian equilibrium, gross substitutes valuations, matroid rank functions}
}

Keywords: Pricing schemes, Walrasian equilibrium, gross substitutes valuations, matroid rank functions
Collection: 31st International Symposium on Algorithms and Computation (ISAAC 2020)
Issue Date: 2020
Date of publication: 04.12.2020


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