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Strategy-Proof Tie-Breaking

  • EHLERS, Lars
  • WESTKAMP, Alexander

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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Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 09-2011.

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Length: 48 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:mtl:montec:09-2011
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  1. EHLERS, Lars & KLAUS, Bettina, 2003. "Efficient Priority Rules," Cahiers de recherche 11-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. EHLERS, Lars, 2006. "Respecting Priorities when Assigning Students to Schools," Cahiers de recherche 04-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2006. "Changing the Boston School Choice Mechanism," Levine's Bibliography 122247000000001022, UCLA Department of Economics.
  4. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
  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. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, vol. 98(3), pages 669-89, June.
  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. 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.
  9. Atila Abdulkadiroglu & Tayfun Smez, 2003. "School Choice: A Mechanism Design Approach," Discussion Papers 0203-18, Columbia University, Department of Economics.
  10. 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.
  11. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
  12. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2009. "Individual versus group strategy proofedness: when do they coincide?," Working Papers 372, Barcelona Graduate School of Economics.
  13. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
  14. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
  15. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
  16. 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.
  17. 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.
  18. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
  19. Ehlers, Lars & Erdil, Aytek, 2010. "Efficient assignment respecting priorities," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1269-1282, May.
  20. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
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