IDEAS home Printed from https://ideas.repec.org/p/cor/louvco/2004060.html
   My bibliography  Save this paper

On blocking coalitions : linking Mas-Colell with Grodal-Schmeidler-Vind

Author

Listed:
  • GREENBERG, Joseph
  • WEBER, Shlomo
  • YAMAZAKI, Akira

Abstract

In this paper we investigate the question of how many coalitions of a given relative size would block a non-Walrasian allocation in large finite economies. It is shown that in finite economies, if a Pareto optimal allocation is bounded away from being Walrasian, then, for any two numbers [alpha], [beta], between 0 and 1, the proportion of blocking coalitions in the set of all coalitions with relative size between [alpha] and [beta], is arbitrarily close to 1/2, as the number of individuals in the economy becomes large.

Suggested Citation

  • GREENBERG, Joseph & WEBER, Shlomo & YAMAZAKI, Akira, 2004. "On blocking coalitions : linking Mas-Colell with Grodal-Schmeidler-Vind," LIDAM Discussion Papers CORE 2004060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2004060
    as

    Download full text from publisher

    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2004.html
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kirman, Alan P & Oddou, Claude & Weber, Shlomo, 1986. "Stochastic Communication and Coalition Formation," Econometrica, Econometric Society, vol. 54(1), pages 129-138, January.
    2. Schmeidler, David, 1972. "A Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 579-580, May.
    3. Rustichini, Aldo & Yannelis, Nicholas C., 1991. "Edgeworth's conjecture in economies with a continuum of agents and commodities," Journal of Mathematical Economics, Elsevier, vol. 20(3), pages 307-326.
    4. Greenberg, Joseph & Weber, Shlomo, 1983. "A core equivalence theorem with an arbitrary communication structure," Journal of Mathematical Economics, Elsevier, vol. 11(1), pages 43-55, January.
    5. Mas-Colell, Andreu, 1978. "A note on the core equivalence theorem : How many blocking coalitions are there?," Journal of Mathematical Economics, Elsevier, vol. 5(3), pages 207-215, December.
    6. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    7. HILDENBRAND, Werner, 1968. "The core of an economy with a measure space of economic agents," LIDAM Reprints CORE 26, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Grodal, Birgit, 1972. "A Second Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 581-583, May.
    9. Vind, Karl, 1972. "A Third Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 585-586, May.
    10. Shitovitz, Benyamin, 1983. "The proportion of blocking coalitions in atomless economies," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 247-255, December.
    11. Maria Gabriella Graziano, 2000. "Measuring the set of blocking coalitions in infinite dimensional economies," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 23(2), pages 101-120.
    12. Yamazaki, Akira, 1984. "Walras degrees and probability of a blocking coalition at pareto allocations," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 105-121, October.
    13. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-1487, November.
    14. W. Hildenbrand, 1968. "The Core of an Economy with a Measure Space of Economic Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(4), pages 443-452.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Giovanna Bimonte, 2013. "A General Coalition Structure: Some Equivalence Results," Working Papers 3_230, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Greenberg, Joseph & Weber, Shlomo & Yamazaki, Akira, 2007. "On blocking coalitions: Linking Mas-Colell with Grodal-Schmeidler-Vind," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 615-628, June.
    2. Giovanna Bimonte & Maria Graziano, 2009. "The measure of blocking coalitions in differential information economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 331-350, February.
    3. Yusuke Kamishiro & Roberto Serrano & Myrna Wooders, 2021. "Monopolists of scarce information and small group effectiveness in large quasilinear economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 801-827, December.
    4. Basile, Achille & Graziano, Maria Gabriella, 2001. "On the edgeworth's conjecture in finitely additive economies with restricted coalitions," Journal of Mathematical Economics, Elsevier, vol. 36(3), pages 219-240, December.
    5. Robert P. Gilles, 2018. "The Core of an Economy with an Endogenous Social Division of Labour," Papers 1809.01470, arXiv.org.
    6. Achille Basile & Robert P. Gilles & Maria Gabriella Graziano & Marialaura Pesce, 2021. "The Core of economies with collective goods and a social division of labour," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1085-1119, April.
    7. Inoue, Tomoki, 2005. "Do pure indivisibilities prevent core equivalence? Core equivalence theorem in an atomless economy with purely indivisible commodities only," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 571-601, August.
    8. Wei He & Nicholas C. Yannelis, 2013. "A New Perspective on Rational Expectations," Economics Discussion Paper Series 1317, Economics, The University of Manchester.
    9. He, Wei & Yannelis, Nicholas C., 2015. "Equilibrium theory under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 86-95.
    10. Bhowmik, Anuj & Saha, Sandipan, 2022. "On blocking mechanisms in economies with club goods," MPRA Paper 114928, University Library of Munich, Germany.
    11. Bhowmik, Anuj & Cao, Jiling, 2011. "Infinite dimensional mixed economies with asymmetric information," MPRA Paper 35618, University Library of Munich, Germany.
    12. Wooders, Myrna H., 2001. "Some corrections to claims about the literature in Engl and Scotchmer (1996)," Journal of Mathematical Economics, Elsevier, vol. 36(4), pages 295-309, December.
    13. Bhowmik, Anuj & Cao, Jiling, 2012. "Blocking efficiency in an economy with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 396-403.
    14. Furth, Dave, 1998. "The core of the inductive limit of a direct system of economies with a communication structure," Journal of Mathematical Economics, Elsevier, vol. 30(4), pages 433-472, November.
    15. 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.
    16. Evren, Özgür & Hüsseinov, Farhad, 2008. "Theorems on the core of an economy with infinitely many commodities and consumers," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1180-1196, December.
    17. Pesce, Marialaura, 2014. "The veto mechanism in atomic differential information economies," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 33-45.
    18. Herves-Beloso, Carlos & Moreno-Garcia, Emma & Yannelis, Nicholas C., 2005. "An equivalence theorem for a differential information economy," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 844-856, November.
    19. Hervés-Estévez, Javier & Moreno-García, Emma, 2014. "On bargaining sets for finite economies," MPRA Paper 62303, University Library of Munich, Germany, revised 18 Jul 2014.
    20. Giovanna Bimonte, 2013. "A General Coalition Structure: Some Equivalence Results," Working Papers 3_230, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cor:louvco:2004060. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Alain GILLIS (email available below). General contact details of provider: https://edirc.repec.org/data/coreebe.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.