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Top Trading with Fixed Tie-Breaking in Markets with Indivisible Goods

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  • EHLERS, Lars

Abstract

We study markets with indivisible goods where monetary compensations are not possible. Each individual is endowed with an object and a preference relation over all objects. When preferences are strict, Gale's top trading cycle algorithm finds the unique core allocation. When preferences are not necessarily strict, we use an exogenous profile of tie-breakers to resolve any ties in individuals' preferences and apply Gale's top trading cycle algorithm for the resulting profile of strict preferences. We provide a foundation of these simple extensions of Gale's top trading cycle algorithm from strict preferences to weak preferences. We show that Gale's top trading cycle algorithm with fixed tie-breaking is characterized by individual rationality, strategy-proofness, weak efficiency, non-bossiness, and consistency. Our result supports the common practice in applications to break ties in weak preferences using some fixed exogenous criteria and then to use a “good and simple” rule for the resulting strict preferences. This reinforces the market-based approach even in the presence of indifferences because always competitive allocations are chosen.

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File URL: https://papyrus.bib.umontreal.ca/jspui/handle/1866/8258
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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2012-02.

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Length: 25 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:mtl:montde:2012-02

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Keywords: Indivisible goods; top trading cycles; indifferences; fixed tie-breaking.;

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References

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  1. Atila Abdulkadiroglu & Tayfun Smez, 2003. "School Choice: A Mechanism Design Approach," Discussion Papers 0203-18, Columbia University, Department of Economics.
  2. 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.
  3. Bird, Charles G., 1984. "Group incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 14(4), pages 309-313.
  4. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
  5. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
  6. 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).
  7. Crawford, Vincent P., 1991. "Comparative statics in matching markets," Journal of Economic Theory, Elsevier, vol. 54(2), pages 389-400, August.
  8. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
  9. Ehlers, Lars, 2004. "Monotonic and implementable solutions in generalized matching problems," Journal of Economic Theory, Elsevier, vol. 114(2), pages 358-369, February.
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