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- W3116827133 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 Duetting and Vegh in 2017. We further formalize a weighted variant of the conjecture of Duetting and Vegh, 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." @default.
- W3116827133 created "2021-01-05" @default.
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- W3116827133 date "2020-12-01" @default.
- W3116827133 modified "2023-09-25" @default.
- W3116827133 title "Market Pricing for Matroid Rank Valuations" @default.
- W3116827133 doi "https://doi.org/10.4230/lipics.isaac.2020.39" @default.
- W3116827133 hasPublicationYear "2020" @default.
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