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The Division Problem under Constraints

  • Gustavo Bergantiños
  • Jordi Massó
  • Alejandro Neme

The division problem under constraints consists of allocating a given amount of an homogeneous and perfectly divisible good among a subset of agents with single-peaked preferences on an exogenously given interval of feasible allotments. We characterize axiomatically the family of extended uniform rules proposed to solve the division problem under constraints. Rules in this family extend the uniform rule used to solve the classical division problem without constraints. We show that the family of all extended uniform rules coincides with the set of rules satisfying efficiency, strategy-proofness, equal treatment of equals, bound monotonicity, consistency, and independence of irrelevant coalitions.

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Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 745.

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Date of creation: Dec 2013
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Handle: RePEc:bge:wpaper:745
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  1. Thomson, W., 1991. "Population-Monotonic Solutions to the Problem of Fair Division when Preferences are Single-Peaked," RCER Working Papers 302, University of Rochester - Center for Economic Research (RCER).
  2. Gustavo Berganti�os & Jordi Massé and Alejandro Neme, 2010. "The Division Problem with Voluntary Participation," Working Papers 437, Barcelona Graduate School of Economics.
  3. Thomson, W, 1995. "The Replacement Principle in Economies with Indivisible Goods," RCER Working Papers 403, University of Rochester - Center for Economic Research (RCER).
  4. Dagan, Nir, 1996. "A Note on Thomson's Characterizations of the Uniform Rule," Journal of Economic Theory, Elsevier, vol. 69(1), pages 255-261, April.
  5. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August.
  6. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  7. Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2012. "The division problem with maximal capacity constraints," SERIEs, Spanish Economic Association, vol. 3(1), pages 29-57, March.
  8. Moulin, Herve, 1999. "Rationing a Commodity along Fixed Paths," Journal of Economic Theory, Elsevier, vol. 84(1), pages 41-72, January.
  9. Schummer, James & Thomson, William, 1997. "Two derivations of the uniform rule and an application to bankruptcy," Economics Letters, Elsevier, vol. 55(3), pages 333-337, September.
  10. Özgür Kıbrıs, 2003. "Constrained allocation problems with single-peaked preferences: An axiomatic analysis," Social Choice and Welfare, Springer, vol. 20(3), pages 353-362, 06.
  11. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  12. EHLERS, Lars, 2001. "On Fixed-Path Rationing Methods," Cahiers de recherche 2001-24, Universite de Montreal, Departement de sciences economiques.
  13. Lars Ehlers, 2002. "Resource-monotonic allocation when preferences are single-peaked," Economic Theory, Springer, vol. 20(1), pages 113-131.
  14. Sonmez, Tayfun, 1994. "Consistency, monotonicity, and the uniform rule," Economics Letters, Elsevier, vol. 46(3), pages 229-235, November.
  15. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
  16. Manjunath, Vikram, 2012. "When too little is as good as nothing at all: Rationing a disposable good among satiable people with acceptance thresholds," Games and Economic Behavior, Elsevier, vol. 74(2), pages 576-587.
  17. Ching, Stephen, 1992. "A simple characterization of the uniform rule," Economics Letters, Elsevier, vol. 40(1), pages 57-60, September.
  18. Salvador Barberà, 2010. "Strategy-proof social choice," UFAE and IAE Working Papers 828.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
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