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The Difference Indifference Makes in Strategy-Proof Allocation of Objects

  • Paula Jaramillo

    ()

  • Vikram Manjunath

We study the problem of allocating objects among people. We consider cases where each object is initially owned by someone, no object is initially owned by anyone, and combinations of the two. The problems we look at are those where each person has a need for exactly one object and initially owns at most one object (also known as house allocation with existing tenants"). We split with most of the existing literature on this topic by dropping the assumption that people can always strictly rank the objects. We show that, without this assumption, problems in which either some or all of the objects are not initially owned are equivalent to problems where each object is initially owned by someone. Thus, it suffices to study problems of the latter type.We ask if there are efficient rules that provide incentives for each person not only to participate (rather than stay home with what he owns), but also to state his preferences honestly. Our main contribution is to show that the answer is positive. The intuitive "top trading cycles" algorithm provides the only such rule for environments where people are never indifferent (Ma 1994). We generalize this algorithm in a way that allows for indifference without compromising on efficiency and incentives."

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File URL: http://economia.uniandes.edu.co/publicaciones/dcede2011-17.pdf
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Paper provided by UNIVERSIDAD DE LOS ANDES-CEDE in its series DOCUMENTOS CEDE with number 008746.

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Length: 57
Date of creation: 03 Apr 2011
Date of revision:
Handle: RePEc:col:000089:008746
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  1. ALCALDE-UNZU, Jorge & MOLIS, Elena, 2009. "Exchange of indivisible goods and indifferences: the Top Trading Absorbing Sets mechanisms," CORE Discussion Papers 2009062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Miyagawa, Eiichi, 2002. "Strategy-Proofness and the Core in House Allocation Problems," Games and Economic Behavior, Elsevier, vol. 38(2), pages 347-361, February.
  3. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
  4. Marek Pycia & M. Utku Ünver, 2009. "Incentive Compatible Allocation and Exchange of Discrete Resources," Boston College Working Papers in Economics 715, Boston College Department of Economics, revised 11 Mar 2014.
  5. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
  6. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
  7. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
  8. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  9. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer, vol. 23(1), pages 75-83.
  10. Thomas Quint & Jun Wako, 2004. "On Houseswapping, the Strict Core, Segmentation, and Linear Programming," Yale School of Management Working Papers ysm373, Yale School of Management.
  11. Tayfun Sonmez, 1999. "Strategy-Proofness and Essentially Single-Valued Cores," Econometrica, Econometric Society, vol. 67(3), pages 677-690, May.
  12. Bogomolnaia, Anna & Deb, Rajat & Ehlers, Lars, 2005. "Strategy-proof assignment on the full preference domain," Journal of Economic Theory, Elsevier, vol. 123(2), pages 161-186, August.
  13. Bird, Charles G., 1984. "Group incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 14(4), pages 309-313.
  14. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
  15. Sönmez, Tayfun & Ünver, M. Utku, 2010. "House allocation with existing tenants: A characterization," Games and Economic Behavior, Elsevier, vol. 69(2), pages 425-445, July.
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