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Fair and efficient student placement with couples

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  • Bettina Klaus

    ()

  • Flip Klijn

    ()

Abstract

We study situations of allocating positions to students based on priorities. An example is the assignment of medical students to hospital residencies on the basis of entrance exams. For markets without couples, e.g., for undergraduate student placement, acyclicity is a necessary and sufficient condition for the existence of a fair and efficient placement mechanism (Ergin, 2002). We show that in the presence of couples acyclicity is still necessary, but not sufficient. A second necessary condition is priority-togetherness of couples. A priority structure that satisfies both necessary conditions is called pt-acyclic. For student placement problems where all quotas are equal to one we characterize ptacyclicity and show that it is a sufficient condition for the existence of a fair and efficient placement mechanism. If in addition to pt-acyclicity we require reallocation- and vacancyfairness for couples, the so-called dictator-bidictator placement mechanism is the unique fair and efficient placement mechanism. Finally, for general student placement problems, we show that pt-acyclicity may not be sufficient for the existence of a fair and efficient placement mechanism. We identify a sufficient condition such that the so-called sequential placement mechanism produces a fair and efficient allocation.

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 36 (2007)
Issue (Month): 2 (October)
Pages: 177-207

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Handle: RePEc:spr:jogath:v:36:y:2007:i:2:p:177-207

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Related research

Keywords: Student placement; Fairness; Efficiency; Couples; Acyclic priority structure; D61; D63; D70; C78;

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  1. Lars Ehlers & Bettina Klaus, 2007. "Consistent House Allocation," Economic Theory, Springer, vol. 30(3), pages 561-574, March.
  2. EHLERS, Lars & KLAUS, Bettina, 2003. "Efficient Priority Rules," Cahiers de recherche 11-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Lars Ehlers & Bettina Klaus, 2003. "Resource-Monotonicity for House Allocation," Working Papers 33, Barcelona Graduate School of Economics.
  4. Bettina Klaus & Flip Klijn & Jordi Massó, 2003. "Some Things Couples always wanted to know about stable matchings (but were afraid to ask)," Working Papers 78, Barcelona Graduate School of Economics.
  5. Bettina Klaus & Flip Klijn, 2004. "Stable Matchings and Preferences of Couples," Working Papers 117, Barcelona Graduate School of Economics.
  6. Bettina Klaus & Flip Klijn, 2004. "Paths to Stability for Matching Markets with Couples," Working Papers 156, Barcelona Graduate School of Economics.
  7. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
  8. 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.
  9. 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.
  10. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
  11. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
  12. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
  13. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
  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, 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, vol. 92(6), pages 991-1016, December.
  16. Ergin, Haluk I., 2000. "Consistency in house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 77-97, August.
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