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The Nakamura Theorem for Coalition Structures of Quota Games

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  • Deb, Rajat
  • Weber, Shlomo
  • Winter, Eyal

Abstract

This paper considers a model of society [script S] with a finite number of individuals, n, a finite set off alternatives, Omega, effective coalitions that must contain an a priori given number q of individuals. Its purpose is to extend the Nakamura Theorem (1979) to the quota games where individuals are allowed to form groups of size q which are smaller than the grand coalition. Our main result determines the upper bound on the number of alternatives which would guarantee, for a given n and q, the existence of a stable coalition structure for any profile of complete transitive preference relations. Our notion of stability, [script S]-equilibrium, introduced by Greenberg-Weber (1993), combines both free entry and free mobility and represents the natural extension of the core to improper or non-superadditive games where coalition structures, and not only the grand coalition, are allowed to form.

Suggested Citation

  • Deb, Rajat & Weber, Shlomo & Winter, Eyal, 1996. "The Nakamura Theorem for Coalition Structures of Quota Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 189-198.
    • Handle: RePEc:spr:jogath:v:25:y:1996:i:2:p:189-98
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    Cited by:

    1. Josep Freixas & Sascha Kurz, 2019. "Bounds for the Nakamura number," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(4), pages 607-634, April.
    2. Le Breton, Michel & Weber, Shlomo, 2004. "Group Formation with Heterogeneous Sets," IDEI Working Papers 288, Institut d'Économie Industrielle (IDEI), Toulouse.

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