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Strategy-Proof Tie-Breaking

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  • EHLERS, Lars
  • WESTKAMP, Alexander

Abstract

We study a general class of priority-based allocation problems with weak priority orders and identify conditions under which there exists a strategy-proof mechanism which always chooses an agent-optimal stable, or constrained efficient, matching. A priority structure for which these two requirements are compatible is called solvable. For the general class of priority-based allocation problems with weak priority orders, we introduce three simple necessary conditions on the priority structure. We show that these conditions completely characterize solvable environments within the class of indifferences at the bottom (IB) environments, where ties occur only at the bottom of the priority structure. This generalizes and unifies previously known results on solvable and unsolvable environments established in school choice, housing markets and house allocation with existing tenants. We show how the previously known solvable cases can be viewed as extreme cases of solvable environments. For sufficiency of our conditions we introduce a version of the agent-proposing deferred acceptance algorithm with exogenous and preference-based tie-breaking.

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File URL: https://papyrus.bib.umontreal.ca/jspui/handle/1866/4002
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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2011-07.

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Length: 48 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:mtl:montde:2011-07

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Keywords: Weak priorities; stability; constrained eciency; strategy-proofness.;

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References

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  1. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
  2. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  3. 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.
  4. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
  5. Budish, Eric & Cantillon, Estelle, 2010. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," CEPR Discussion Papers 7641, C.E.P.R. Discussion Papers.
  6. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
  7. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2009. "Individual versus group strategy proofedness: when do they coincide?," Working Papers 372, Barcelona Graduate School of Economics.
  8. Aytek Erdil & Haluk Ergin, 2007. "What`s the Matter with Tie-breaking? Improving Efficiency in School Choice," Economics Series Working Papers 349, University of Oxford, Department of Economics.
  9. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
  10. Ehlers, Lars & Erdil, Aytek, 2010. "Efficient assignment respecting priorities," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1269-1282, May.
  11. 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.
  12. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
  13. Roth, Alvin E, 1986. "On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets," Econometrica, Econometric Society, vol. 54(2), pages 425-27, March.
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