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

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  • GREENBERG, Joseph
  • WEBER, Shlomo
  • YAMAZAKI, Akira
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    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.

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    Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2004060.

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    Date of creation: 00 Sep 2004
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    Handle: RePEc:cor:louvco:2004060

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    1. Shitovitz, Benyamin, 1983. "The proportion of blocking coalitions in atomless economies," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 247-255, December.
    2. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-87, November.
    3. Schmeidler, David, 1972. "A Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 579-80, May.
    4. 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.
    5. 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.
    6. Maria Gabriella Graziano, 2000. "Measuring the set of blocking coalitions in infinite dimensional economies," Decisions in Economics and Finance, Springer, vol. 23(2), pages 101-120.
    7. Kirman, Alan P & Oddou, Claude & Weber, Shlomo, 1986. "Stochastic Communication and Coalition Formation," Econometrica, Econometric Society, vol. 54(1), pages 129-38, January.
    8. 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.
    9. Vind, Karl, 1972. "A Third Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 585-86, May.
    10. Grodal, Birgit, 1972. "A Second Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 581-83, May.
    11. 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.
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