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A Note on Kelso and Crawford's Gross Substitutes Condition

Authors:

Satoru Fujishige,

Zaifu YangAuthors Info & Claims

Mathematics of Operations Research, Volume 28, Issue 3

Pages 463 - 469

https://doi.org/10.1287/moor.28.3.463.16393

Published: 01 July 2003 Publication History

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Abstract

In their 1982 article, Kelso and Crawford proposed a gross substitutes condition for the existence of core (and equilibrium) in a two-sided matching model. Since then, this condition has often been used in the literature on matching models and equilibrium models in the presence of indivisibilities. In this paper we prove that a reservation value (or utility) function satisfies the gross substitutes condition if and only if it is anM?-concave function defined on the unit-hypercube, which is a discrete concave function recently introduced by Murota and Shioura (1999).

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Chen XLi M(2024)S-Convexity and Gross SubstitutabilityOperations Research10.1287/opre.2022.239472:3(1242-1254)Online publication date: 1-May-2024
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Fotakis DMatuschke JPapadigenopoulos O(2024)A constant-factor approximation for generalized malleable scheduling under -concave processing speedsMathematical Programming: Series A and B10.1007/s10107-023-02054-z206:1-2(515-539)Online publication date: 1-Jul-2024
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A Note on Kelso and Crawford's Gross Substitutes Condition

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cover image Mathematics of Operations Research

Mathematics of Operations Research Volume 28, Issue 3

July 2003

214 pages

ISSN:0364-765X

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INFORMS

Linthicum, MD, United States

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Published: 01 July 2003

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Chen XLi M(2024)S-Convexity and Gross SubstitutabilityOperations Research10.1287/opre.2022.239472:3(1242-1254)Online publication date: 1-May-2024
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Kizilkale CVohra R(2024)Constrained Trading NetworksMathematics of Operations Research10.1287/moor.2023.136249:1(430-440)Online publication date: 1-Feb-2024
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Tatonnement beyond gross substitutes?: gradient descent to the rescue

Polynomial-Time Approximation Schemes for Maximizing Gross Substitutes Utility Under Budget Constraints

Simple primal-dual auctions are not possible

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