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Stability of jurisdiction structures under the equal share and median rules

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  • BOGOMOLNAIA, Anna
  • LE BRETON, Michel
  • SAVVATEEV, Alexei
  • WEBER, Shlomo

Abstract

In this paper we consider a model with multiple jurisdictions where each formed jurisdiction selects a public project from the given uni-dimensional set, equally shares its cost among its members and places the project at the location of its median resident. We examine a cooperative concept of core stability and a non-cooperative notion of Nash stability of jurisdiction structures. We first consider hedonic games, where each jurisdiction chooses the mean of the extreme points of its median set, and show that both stability notions may lead to an empty set of stable jurisdiction structures. We demonstrate that in a quasi-hedonic set-up, where jurisdictions are allowed to pick any selection from the median set, there is a Nash stable partition, while a core stable partition may still fail to exist. We also consider the equidistant societies and show the existence of both types of stable partitions in this case. Finally, we examine stratification properties of stable partitions.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2005032.

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Date of creation: 00 2005
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Handle: RePEc:cor:louvco:2005032

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Keywords: equal share rule; median rule; jurisdictions; core and Nash stable partitions;

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References

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  1. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 161-182, October.
  2. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  3. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1998. "Equilibrium in a Finite Local Public Goods Economy," Journal of Economic Theory, Elsevier, vol. 79(2), pages 224-244, April.
  4. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer, vol. 18(1), pages 135-153.
  5. Casella, Alessandra, 1996. "The Role of Market Size in the Formation of Jurisdictions," CEPR Discussion Papers 1429, C.E.P.R. Discussion Papers.
  6. Dreze, Jacques & Le Breton, Michel & Weber, Shlomo, 2006. "Rawlsian Pricing of Access to Public Facilities: A Unidimensional Illustration," IDEI Working Papers 409, Institut d'Économie Industrielle (IDEI), Toulouse.
  7. Mas-Colell, Andreu, 1980. "Efficiency and Decentralization in the Pure Theory of Public Goods," The Quarterly Journal of Economics, MIT Press, vol. 94(4), pages 625-41, June.
  8. Philippe JEHIEL & Suzanne SCOTCHMER, 1997. "Free Mobility and the Optimal Number of Jurisdictions," Annales d'Economie et de Statistique, ENSAE, issue 45, pages 219-231.
  9. Jehiel, Philippe & Scotchmer, Suzanne, 2001. "Constitutional Rules of Exclusion in Jurisdiction Formation," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 393-413, April.
  10. Alberto Alesina & Enrico Spolaore, 1995. "On the Number and Size of Nations," NBER Working Papers 5050, National Bureau of Economic Research, Inc.
  11. Haimanko, Ori & Le Breton, Michel & Weber, Shlomo, 2005. "Transfers in a polarized country: bridging the gap between efficiency and stability," Journal of Public Economics, Elsevier, vol. 89(7), pages 1277-1303, July.
  12. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  13. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, vol. 38(1), pages 101-117, February.
  14. Le Breton, Michel & Weber, Shlomo, 2003. "The Art of Making Everybody Happy : How to Prevent a Secession," IDEI Working Papers 164, Institut d'Économie Industrielle (IDEI), Toulouse.
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Citations

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Cited by:
  1. Alexei Savvateev & Jacques Drèze & Michel Le Breton & Shlomo Weber, 2007. "“Almost” Subsidy-free Spatial Pricing in a Multi-dimensional Setting," Working Papers 2007.68, Fondazione Eni Enrico Mattei.
  2. BOGOMOLNAIA, Anna & LE BRETON, Michel & SAVVATEEV, Alexei & WEBER, Shlomo, 2006. "Stability under unanimous consent, free mobility and core," CORE Discussion Papers 2006007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Iehlé, Vincent, 2007. "The Core-Partition of Hedonic Games," Economics Papers from University Paris Dauphine 123456789/87, Paris Dauphine University.
  4. Dahlby, Bev, 2009. "Too Many Municipalities?," Working Papers 2009-18, University of Alberta, Department of Economics.
  5. Salvador Barberà & Carmen Beviá & Clara Ponsatí, 2014. "Meritocracy, Egalitarianism and the Stability of Majoritarian Organizations," Working Papers 737, Barcelona Graduate School of Economics.
  6. Savvateev, A., 2013. "Coalitional Stability of a "Bipolar World"," Journal of the New Economic Association, New Economic Association, vol. 17(1), pages 10-43.

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