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Local and Global Consistency Properties for Student Placement

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  • Bettina Klaus
  • Flip Klijn

Abstract

In the context of resource allocation on the basis of priorities, Ergin (2002) identifies a necessary and sufficient condition on the priority structure such that the student-optimal stable mechanism satisfies a consistency principle. Ergin (2002) formulates consistency as a local property based on a fixed population of agents and fixed resources -- we refer to this condition as local consistency and to his condition on the priority structure as local acyclicity. We identify a related but stronger necessary and sufficient condition (unit acyclicity) on the priority structure such that the student-optimal stable mechanism satisfies a more standard global consistency property. Next, we provide necessary and sufficient conditions for the student-optimal stable mechanism to satisfy converse consistency principles. We identify a necessary and sufficient condition (local shift-freeness) on the priority structure such that the student-optimal stable mechanism satisfies local converse consistency. Interestingly, local acyclicity implies local shift-freeness and hence the student-optimal stable mechanism more frequently satisfies local converse consistency than local consistency. Finally, in order for the student-optimal stable mechanism to be globally conversely consistent, one again has to impose unit acyclicity on the priority structure. Hence, unit acyclicity is a necessary and sufficient condition on the priority structure for the student-optimal stable mechanism to satisfy global consistency or global converse consistency.

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Bibliographic Info

Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 538.

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Date of creation: Mar 2011
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Handle: RePEc:bge:wpaper:538

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Keywords: acyclicity; consistency; converse consistency; student placement;

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References

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  1. Thomson, W., 1998. "Consistency and its Converse: an Introduction," RCER Working Papers, University of Rochester - Center for Economic Research (RCER) 448, University of Rochester - Center for Economic Research (RCER).
  2. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, Elsevier, vol. 127(1), pages 155-171, March.
  3. Ehlers, Lars & Klaus, Bettina & Papai, Szilvia, 2002. "Strategy-proofness and population-monotonicity for house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 329-339, November.
  4. Lars Ehlers & Bettina Klaus, 2003. "Resource-Monotonicity for House Allocation Problems," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 566.03, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  5. Ehlers,Lars & Klaus,Bettina, 2005. "Consistent House Allocation," Research Memorandum, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) 007, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  6. EHLERS, Lars & KLAUS, Bettina, 2003. "Efficient Priority Rules," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 11-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  7. Thomson, William & Zhou, Lin, 1993. "Consistent Solutions in Atomless Economies," Econometrica, Econometric Society, Econometric Society, vol. 61(3), pages 575-87, May.
  8. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, Econometric Society, vol. 70(6), pages 2489-2497, November.
  9. Sasaki, Hiroo & Toda, Manabu, 1992. "Consistency and characterization of the core of two-sided matching problems," Journal of Economic Theory, Elsevier, Elsevier, vol. 56(1), pages 218-227, February.
  10. Ergin, Haluk I., 2000. "Consistency in house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 77-97, August.
  11. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, Elsevier, vol. 36(2), pages 277-288, August.
  12. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 92(6), pages 991-1016, December.
  13. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, Elsevier, vol. 105(2), pages 298-317, August.
  14. Lars Ehlers & Bettina Klaus, 2003. "Resource-Monotonicity for House Allocation," Working Papers 33, Barcelona Graduate School of Economics.
  15. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, Elsevier, vol. 84(1), pages 73-94, January.
  16. İpek Özkal-Sanver, 2013. "Minimal conversely consistent extension of the men-optimal solution," Social Choice and Welfare, Springer, Springer, vol. 40(1), pages 89-99, January.
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Cited by:
  1. Rodrigo Velez, 2014. "Consistent strategy-proof assignment by hierarchical exchange," Economic Theory, Springer, Springer, vol. 56(1), pages 125-156, May.

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