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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. Eric Friedman & Moulin, Herve, 1995. "Three Methods to Share Joint Costs or Surplus," Working Papers 95-38, Duke University, Department of Economics.
  2. Lars Ehlers & Bettina Klaus, 2003. "Efficient Priority Rules," Working Papers 103, Barcelona Graduate School of Economics.
  3. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, Junio.
  4. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  5. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, vol. 102(5), pages 2237-71, August.
  6. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
  7. Moulin, Herve & Sprumont, Yves, 2003. "On Demand Responsiveness in Additive Cost Sharing," Working Papers 2003-10, Rice University, Department of Economics.
  8. Atila Abdulkadiroglu & Parag Pathak & Alvin E. Roth & Tayfun Sonmez, 2006. "Changing the Boston School Choice Mechanism," NBER Working Papers 11965, National Bureau of Economic Research, Inc.
  9. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
  10. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
  11. Moulin, Herve & Sprumont, Yves, 2006. "Responsibility and cross-subsidization in cost sharing," Games and Economic Behavior, Elsevier, vol. 55(1), pages 152-188, April.
  12. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
  13. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
  14. Hervé Moulin, 1995. "On Additive Methods To Share Joint Costs," The Japanese Economic Review, Japanese Economic Association, vol. 46(4), pages 303-332, December.
  15. Eric J. Friedman, 2004. "Paths and consistency in additive cost sharing," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 501-518, 08.
  16. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
  17. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
  18. Ehlers, Lars & Erdil, Aytek, 2010. "Efficient assignment respecting priorities," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1269-1282, May.
  19. 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.
  20. 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.
  21. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 75-83.
  22. 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.
  23. EHLERS, Lars, 2006. "Respecting Priorities when Assigning Students to Schools," Cahiers de recherche 2006-04, Universite de Montreal, Departement de sciences economiques.
  24. 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.
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