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On Vind’s theorem for an economy with atoms and infinitely many commodities

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  • Bhowmik, Anuj
  • Graziano, Maria Gabriella

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.

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  • Bhowmik, Anuj & Graziano, Maria Gabriella, 2015. "On Vind’s theorem for an economy with atoms and infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 26-36.
  • Handle: RePEc:eee:mateco:v:56:y:2015:i:c:p:26-36
    DOI: 10.1016/j.jmateco.2014.11.005
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Anuj Bhowmik & Maria Gabriella Graziano, 2018. "Blocking Coalitions and Fairness in Asset Markets and Asymmetric Information Economies," CSEF Working Papers 510, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    2. Francesca Centrone & Anna Martellotti, 2016. "Coalitional extreme desirability in finitely additive exchange economies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 17-34, April.
    3. Anuj Bhowmik, 2015. "Core and coalitional fairness: the case of information sharing rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(3), pages 461-494, November.
    4. repec:kap:jeczfn:v:123:y:2018:i:2:d:10.1007_s00712-017-0543-7 is not listed on IDEAS
    5. Achille Basile & Maria Gabriella Graziano & Ciro Tarantino, 2018. "Coalitional fairness with participation rates," Journal of Economics, Springer, vol. 123(2), pages 97-139, March.

    More about this item

    Keywords

    Coalitions; Aubin coalitions; Core; Cone conditions;

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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