Market pricing for matroid rank valuations

Kristóf Bérczi, Naonori Kakimura, Yusuke Kobayashi

研究成果: Conference contribution

抄録

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.

本文言語English
ホスト出版物のタイトル31st International Symposium on Algorithms and Computation, ISAAC 2020
編集者Yixin Cao, Siu-Wing Cheng, Minming Li
出版社Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ページ391-3915
ページ数3525
ISBN(電子版)9783959771733
DOI
出版ステータスPublished - 2020 12
イベント31st International Symposium on Algorithms and Computation, ISAAC 2020 - Virtual, Hong Kong, China
継続期間: 2020 12 142020 12 18

出版物シリーズ

名前Leibniz International Proceedings in Informatics, LIPIcs
181
ISSN(印刷版)1868-8969

Conference

Conference31st International Symposium on Algorithms and Computation, ISAAC 2020
国/地域China
CityVirtual, Hong Kong
Period20/12/1420/12/18

ASJC Scopus subject areas

  • ソフトウェア

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