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Coalitional Stability of a "Bipolar World"

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  • Savvateev, A.

    (New Economic School, Moscow, Russia)

Abstract

The model considered in the paper is devoted to the analysis of local public good provision in the economy the consumers of which are exogenously divided to a finite number of types. Each type is represented by a continuum of identical agents and is described by a certain optimal bundle of characteristics of a public good to be consumed; departure from the optimal point in the space of characteristics involves an extra cost for each individual. Masses of consumers of each type are also exogenous to the model. A solution concept is introduced which is a partition of the set of individuals into disjoint groups, a priori without correlation to the division into types. Each group has access to one and the same variety of a local public good, the latter being selected via the median principle, i.e. minimizing total "disagreement cost" of members of that group. Partition is coalitionary stable if no coalition (i.e. nonempty measurable subset) of agents can Pareto improve itself via the formation of a new jurisdiction and choosing a variety of a good according to the same median principle. The case of the two types of consumers is fully analyzed. For each configuration of parameters of the model, all stable partitions are specified. It turns out that, for certain combinations of parameters, there are no stable partitions, and which could be even more surprising, there exist economies for which the only stable partition divides one of the two types between the two groups. Such a situation is impossible if one looks for optimal, not stable, solutions.

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Bibliographic Info

Article provided by New Economic Association in its journal Journal of the New Economic Association.

Volume (Year): 17 (2013)
Issue (Month): 1 ()
Pages: 10-43

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Handle: RePEc:nea:journl:y:2013:i:17:p:10-43

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Related research

Keywords: club goods; horisontal differentiation of preferences; set of partition; median location principle; coalitional stability; equal-share principle;

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References

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  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. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416.
  3. Bogomolnaia, Anna & Le Breton, Michel & Savvateev, Alexei & Weber, Shlomo, 2005. "The Egalitarian Sharing Rule in the Provision of Public Projects," IDEI Working Papers 364, Institut d'Économie Industrielle (IDEI), Toulouse.
  4. Jacques, DREZE & Michel, LE BRETON & Alexei , SAVVATEV & Sholmo, WEBER, 2007. "‘Almost’ subsidy-free spatial pricing in a multi-dimensional setting," Discussion Papers (ECON - Département des Sciences Economiques) 2007030, Université catholique de Louvain, Département des Sciences Economiques.
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  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. Alexei Savvateev & Anna Bogomolnaia & Michel Le Breton & Shlomo Weber, 2005. "The Egalitarian Sharing Rule in Provision of Public Projects," Working Papers 2005.39, Fondazione Eni Enrico Mattei.
  8. BOGOMOLNAIA, Anna & LE BRETON, Michel & SAVVATEEV, Alexei & WEBER, Shlomo, 2005. "Stability of jurisdiction structures under the equal share and median rules," CORE Discussion Papers 2005032, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Michel Le Breton & Shlomo Weber, 2003. "The Art of Making Everybody Happy: How to Prevent a Secession," IMF Staff Papers, Palgrave Macmillan, vol. 50(3), pages 4.
  10. Kolen, Antoon, 1983. "Solving covering problems and the uncapacitated plant location problem on trees," European Journal of Operational Research, Elsevier, vol. 12(3), pages 266-278, March.
  11. 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.
  12. Haimanko, Ori & Le Breton, Michel & Weber, Shlomo, 2004. "Voluntary formation of communities for the provision of public projects," Journal of Economic Theory, Elsevier, vol. 115(1), pages 1-34, March.
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