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Stability and Fairness in Models with a Multiple Membership

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Author Info

  • Michel Le Breton

    ()
    (Universit de Toulouse 1, GREMAQ and IDEI, Toulouse, France)

  • Juan D. Moreno-Ternero

    ()
    (U. de Mlaga, U. Pablo de Olavide y CORE, Universit catholique de Louvain)

  • Alexei Savvateev

    ()
    (New Economic School, Moscow, Russia)

  • Shlomo Weber

    ()
    (Southern Methodist University, USA, and the New Economic School, Moscow, Russia)

Abstract

This article studies a model of coalition formation for the joint production (and finance) of public projects, in which agents may belong to multiple coalitions. We show that, if projects are divisible, there always exists a stable (secession-proof) structure, i.e., a structure in which no coalition would reject a proposed arrangement. When projects are indivisible, stable allocations may fail to exist and, for those cases, we resort to the least core in order to estimate the degree of instability. We also examine the compatibility of stability and fairness in metric environments with indivisible projects, where we also explore the performance of well-known solutions, such as the Shapley value and the nucleolus.

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File URL: http://www.upo.es/serv/bib/wps/econ1016.pdf
File Function: First version, 2010
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Bibliographic Info

Paper provided by Universidad Pablo de Olavide, Department of Economics in its series Working Papers with number 10.16.

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Length: 44 pages
Date of creation: Dec 2010
Date of revision:
Handle: RePEc:pab:wpaper:10.16

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Keywords: Stability; Fairness; Membership; Coalition Formation;

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  1. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, Econometric Society, vol. 50(6), pages 1483-1504, November.
  2. Montero, Maria, 2006. "Noncooperative foundations of the nucleolus in majority games," Games and Economic Behavior, Elsevier, Elsevier, vol. 54(2), pages 380-397, February.
  3. DREZE, Jacques & LE BRETON, Michel & SAVVATEEV, Alexei & WEBER, Shlomo, 2007. "“Almost” subsidy-free spatial pricing in a multi-dimensional setting," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2007047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  6. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 615-35, May.
  7. Javier Arin & Elena Inarra, 2001. "Egalitarian solutions in the core," International Journal of Game Theory, Springer, Springer, vol. 30(2), pages 187-193.
  8. Alberto Alesina & Ignazio Angeloni & Federico Etro, 2005. "International Unions," American Economic Review, American Economic Association, American Economic Association, vol. 95(3), pages 602-615, June.
  9. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521681599.
  10. 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.
  11. Kolen, Antoon, 1983. "Solving covering problems and the uncapacitated plant location problem on trees," European Journal of Operational Research, Elsevier, Elsevier, vol. 12(3), pages 266-278, March.
  12. Jens Leth Hougaard & Lars Thorlund-Petersen & Bezalel Peleg, 2001. "On the set of Lorenz-maximal imputations in the core of a balanced game," International Journal of Game Theory, Springer, Springer, vol. 30(2), pages 147-165.
  13. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, Elsevier, vol. 107(2), pages 377-406, December.
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