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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. 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.
  2. Suryapratim Banerjee & Hideo Konishi & Tayfun Sonmez, 1999. "Core in a Simple Coalition Formation Game," Boston College Working Papers in Economics 449, Boston College Department of Economics.
  3. 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.
  4. 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.
  5. Casella, Alessandra, 2001. "The Role of Market Size in the Formation of Jurisdictions," Review of Economic Studies, Wiley Blackwell, vol. 68(1), pages 83-108, January.
  6. 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.
  7. 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.
  8. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  9. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  10. Alesina, Alberto & Spolaore, Enrico, 1997. "On the Number and Size of Nations," The Quarterly Journal of Economics, MIT Press, vol. 112(4), pages 1027-56, November.
  11. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, vol. 38(1), pages 101-117, February.
  12. 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.
  13. 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.
  14. 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.
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Cited by:
  1. Bogomolnaia, Anna & Le Breton, Michel & Savvateev, Alexei & Weber, Shlomo, 2006. "Stability under Unanimous Consent, Free Mobility and Core," IDEI Working Papers 413, Institut d'Économie Industrielle (IDEI), Toulouse.
  2. Vincent Iehlé, 2005. "The core-partition of hedonic games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00197528, HAL.
  3. DREZE, Jacques & LE BRETON, Michel & SAVVATEEV, Alexei & WEBER, Shlomo, 2007. "“Almost” subsidy-free spatial pricing in a multi-dimensional setting," CORE Discussion Papers 2007047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Dahlby, Bev, 2009. "Too Many Municipalities?," Working Papers 2009-18, University of Alberta, Department of Economics.
  5. Savvateev, A., 2013. "Coalitional Stability of a "Bipolar World"," Journal of the New Economic Association, New Economic Association, vol. 17(1), pages 10-43.
  6. Salvador Barberà & Carmen Beviá & Clara Ponsatí, 2014. "Meritocracy, Egalitarianism and the Stability of Majoritarian Organizations," Working Papers 737, Barcelona Graduate School of Economics.

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