A note on the strong core of a market with indivisible goods
type: Item
instance of: scholarly article
title: A note on the strong core of a market with indivisible goods
zbMATH Open document ID: 0563.90013
DOI: 10.1016/0304-4068(84)90017-X
author: Jun Wako
published in: Journal of Mathematical Economics
publication date: 1984-01-01T00:00:00Z
review text: \textit{L. S. Shapley} and \textit{H. E. Scarf} [ibid. 1, 23-37 (1974; Zbl 0281.90014)] studied a market where each agent i owns one indivisible good \(w_ i\), hence resources are \(w=(w_ 1,w_ 2,...,w_ n)\). Each agent has preferences among \(w_ i\), but does not desire more than one good. An allocation \(x=(x_ 1,x_ 2,...,x_ n)\) is a permutation of w. A competitive allocation is defined as usual with a price vector: each agent obtains the good which is best in his budget. An allocation is in the strong core if no coalition can weakly improve by only trading among themselves (at least one agent gets better off and not necessarily all). It is shown in this note that the strong core (which may be empty) is a subset of the competitive allocations, using the method of ''top trading cycles'' as introduced in the above-mentioned paper. An example shows that (normal) core allocations need not be competitive.
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 3898551
zbMATH Keywords: indivisible goods
zbMATH Keywords: competitive allocation
zbMATH Keywords: strong core
zbMATH Keywords: top trading cycles
reviewed by: Claus Weddepohl
MaRDI profile type: Publication
cites work: On cores and indivisibility
cites work: Weak versus strong domination in a market with indivisible goods
cites work: Core and competitive equilibria with indivisibilities
full work available at URL: 0304-4068(84)90017-x
OpenAlex ID: W2163100237
description: scientific article; zbMATH DE number 3898551