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Stability of jurisdiction structures under the equal share and median rules

  • Anna Bogomolnaia
  • Michel Breton
  • Alexei Savvateev
  • Shlomo Weber

    ()

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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File URL: http://hdl.handle.net/10.1007/s00199-006-0198-z
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Article provided by Springer in its journal Economic Theory.

Volume (Year): 34 (2008)
Issue (Month): 3 (March)
Pages: 525-543

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Handle: RePEc:spr:joecth:v:34:y:2008:i:3:p:525-543
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  1. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  2. Dreze, Jacques & Le Breton, Michel & Weber, Shlomo, 2007. "Rawlsian pricing of access to public facilities: A unidimensional illustration," Journal of Economic Theory, Elsevier, vol. 136(1), pages 759-766, September.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, vol. 38(1), pages 101-117, February.
  8. Casella, Alessandra, 1996. "The Role of Market Size in the Formation of Jurisdictions," CEPR Discussion Papers 1429, C.E.P.R. Discussion Papers.
  9. Alberto Alesina & Enrico Spolaore, 1995. "On the Number and Size of Nations," NBER Working Papers 5050, National Bureau of Economic Research, Inc.
  10. 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.
  11. 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.
  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. 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.
  14. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
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