 On Vind’s theorem for an economy with atoms and infinitely many commoditiesAnuj Bhowmik and Maria Graziano Journal of Mathematical Economics, 2015, vol. 56, issue C, 26-36 Abstract: We extend Vind’s classical theorem on the measure of blocking coalitions valid in finite dimensional atomless economies (see Vind (1972)), to include the possibility of infinitely many commodities as well as the presence of atoms. The commodity space is assumed to be an ordered Banach space which has possibly the empty positive cone. The lack of interior points is compensated by an additional assumption of a cone of arbitrage that allows us to use Lyapunov’s convexity theorem in its weak form. The measure space of agents involves both negligible and non negligible traders. The extension is proved in the general class of Aubin coalitions for which a suitable version of Grodal’s result (Grodal (1972)) is also formulated. Our results wish to point out the relevance of cone conditions dealing with blocking coalitions of arbitrary measure or weight. Keywords: Coalitions; Aubin coalitions; Core; Cone conditions (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:56:y:2015:i:c:p:26-36 DOI: 10.1016/j.jmateco.2014.11.005 Access Statistics for this article Journal of Mathematical Economics is currently edited by Atsushi (A.) Kajii More articles in Journal of Mathematical Economics from Elsevier |
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