The bargaining set and the core in mixed markets with atoms and an atomless sector
type: Item
instance of: scholarly article
title: The bargaining set and the core in mixed markets with atoms and an atomless sector
zbMATH Open document ID: 0685.90104
DOI: 10.1016/0304-4068(89)90013-X
published in: Journal of Mathematical Economics
publication date: 1989-01-01T00:00:00Z
review text: Let (T,v) be a cooperative game in characteristic function form. If T is a nonatomic measure space, then the core C(v), the bargaining set B(v), and the set of Walrasian allocations W(v) all coincide, \(C(v)=B(v)=W(v)\). Now suppose that T also contains atoms, and that there exists a commodity whose only owner is an atom. Then \(B(v)=C(v)\), but not necessarily \(=W(v)\). Finally, an example is given in which, if there exists a commodity owned solely by two atoms, \(C(v)=W(v)\subset B(v)\), the latter containment being strict.
Mathematics Subject Classification ID: 91A12
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 91A40
Mathematics Subject Classification ID: 91A07
zbMATH DE Number: 4123558
zbMATH Keywords: nonatomic game
zbMATH Keywords: mixed game
zbMATH Keywords: nonatomic measure space
zbMATH Keywords: core
zbMATH Keywords: bargaining set
zbMATH Keywords: Walrasian allocations
author: Benyamin Shitovitz
MaRDI profile type: Publication
cites work: Markets with a Continuum of Traders
cites work: Q5341355
cites work: Q4121644
cites work: An equivalence theorem for a bargaining set
cites work: Oligopoly in Markets with a Continuum of Traders
full work available at URL: 0304-4068(89)90013-x
OpenAlex ID: W2047231221
description: scientific article; zbMATH DE number 4123558