On Vind's Theorem for an Economy with Atoms and Infinitely Many Commodities

Anuj Bhowmik and Maria Graziano

CSEF Working Papers from Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy

Abstract: We extend Vind's classical theorem on the measure of blocking coalitions valid in finite dimensional atomless economies (see [29]), 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 the 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 ([17]) 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)
JEL-codes: C71 D51 (search for similar items in EconPapers)
Date: 2014-06-03
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: On Vind’s theorem for an economy with atoms and infinitely many commodities (2015)
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