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

Author

Listed:
  • Joseph Greenberg

    (McGill University)

  • Shlomo Weber

    (Southern Methodist University)

  • Akira Yamazaki

    (Meisei University)

Abstract

In this paper we investigate the question of how many coalitions of a given relative size would block a non-Warlasian 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 α and β betwenn 0 and 1, the proportion of blocking coalitions in the set of all coalitions with relative size between α and β, is arbitrarily close to 1/2, as the number of individuals in the economy becomes large.

Suggested Citation

  • Joseph Greenberg & Shlomo Weber & Akira Yamazaki, 2006. "On blocking coalitions: Linking Mas-Colell with Grodal-Schmeidler-Vind," Discussion Papers 2, Meisei University, School of Economics.
    • Handle: RePEc:mei:wpaper:2
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    References listed on IDEAS

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    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. 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.
    4. 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).
    5. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, December.
    6. Shitovitz, Benyamin, 1983. "The proportion of blocking coalitions in atomless economies," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 247-255, December.
    7. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-1487, November.
    8. 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.
    9. 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.
    10. P. Frevert, 1971. "Note," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 269-270.
    11. 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.
    12. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    13. Grodal, Birgit, 1972. "A Second Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 581-583, May.
    14. Vind, Karl, 1972. "A Third Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 585-586, May.
    15. 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.
    16. 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.
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    Cited by:

    1. Yoshiaki Hoshino & Ryuichiro Ishikawa & Akira Yamazaki, 2013. "Unequal Distribution of Powers in a Wicksellian Transfer Game," Discussion Papers 24, Meisei University, School of Economics.
    2. 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.
    3. Akira Yamazaki, 2013. "Production Atomless Economies," Discussion Papers 25, Meisei University, School of Economics.
    4. Robert P. Gilles, 2018. "The Core of an Economy with an Endogenous Social Division of Labour," Papers 1809.01470, arXiv.org.
    5. 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.

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