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Allocation problems with indivisibilities when preferences are single-peaked

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  • Carmen Herrero

    ()

  • Ricardo Martínez

    ()

Abstract

We consider allocation problems with indivisible goods when agents’ preferences are single-peaked. Two natural procedures (up methods and temporary satisfaction methods) are proposed to solve these problems. They are constructed by using priority methods on the cartesian product of agents and integer numbers, interpreted either as peaks or opposite peaks. Thus, two families of solutions arise this way. Our two families of solutions satisfy properties very much related to some well-known properties studied in the case of perfectly divisible goods, and they have a strong relationship with the continuous uniform and equal-distance rules, respectively.

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File URL: http://hdl.handle.net/10.1007/s13209-011-0046-7
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Bibliographic Info

Article provided by Spanish Economic Association in its journal SERIEs.

Volume (Year): 2 (2011)
Issue (Month): 4 (December)
Pages: 453-467

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Handle: RePEc:spr:series:v:2:y:2011:i:4:p:453-467

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Related research

Keywords: Allocation problem; Indivisibilities; Single-peaked preferences; Priority standard; Temporary satisfaction methods; D61; D63; D74;

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References

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  1. Nir Dagan, 1996. "A Note on Thomson's Characterizations of the Uniform Rule," Economic theory and game theory 003, Nir Dagan.
  2. 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.
  3. HERRERO, Carmen & MARTINEZ, Ricardo, 2006. "Balanced allocation methods for claims problems with indivisibilities," CORE Discussion Papers 2006066, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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.
  5. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
  6. Carmen Herrero, 2002. "General allocation problems with single-peaked preferences: path-independence and related topics," Spanish Economic Review, Springer, vol. 4(1), pages 19-40.
  7. Sonmez, Tayfun, 1994. "Consistency, monotonicity, and the uniform rule," Economics Letters, Elsevier, vol. 46(3), pages 229-235, November.
  8. Carmen Herrero Blanco & Ricardo Martínez, 2004. "Egalitarian Rules In Claims Problems With Indivisible Goods," Working Papers. Serie AD 2004-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  9. Thomson, W., 1998. "Consistency and its Converse: an Introduction," RCER Working Papers 448, University of Rochester - Center for Economic Research (RCER).
  10. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
  11. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer, vol. 28(4), pages 511-520.
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Cited by:
  1. Carmen Herrero & Ricardo Martínez, 2008. "Up methods in the allocation of indivisibilities when preferences are single-peaked," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 16(2), pages 272-283, December.

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