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Equilibria under deferred acceptance: Dropping strategies, filled positions, and welfare

Author

Listed:
  • Paula Jaramillo
  • Cagatay Kayi
  • Flip Klijn

Abstract

This paper studies many-to-one matching markets where each student is assigned to a hospital.Each hospital has possibly multiple positions and responsive preferences. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling.Roth and Sotomayor (1990) showed that there can be unstable equilibrium outcomes. We prove that any stable matching can be obtained in some equilibrium. We also show that the exhaustive class of dropping strategies does not necessarily generate the full set of equilibrium outcomes. Finally, we find that the so-called `rural hospital theorem' cannot be extended to the set of equilibrium outcomes and that welfare levels are in general unrelated to the set of stable matchings. Two important consequences are that, contrary to one{to{one matching markets, (a) filled positions depend on the particular equilibrium that is reached and (b) welfare levels are not bounded by the student and hospital-optimal stable matchings (with respect to the true preferences).

Suggested Citation

  • Paula Jaramillo & Cagatay Kayi & Flip Klijn, 2013. "Equilibria under deferred acceptance: Dropping strategies, filled positions, and welfare," Documentos de Trabajo 10724, Universidad del Rosario.
    • Handle: RePEc:col:000092:010724
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    File URL: http://www.urosario.edu.co/economia/documentos/pdf/dt136
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    Cited by:

    1. David Pérez-Castrillo & Marilda Sotomayor, 2017. "The outcome of competitive equilibrium rules in buyer–seller markets when the agents play strategically," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(1), pages 99-119, June.
    2. David Pérez-Castrillo & Marilda Sotomayor, 2017. "On the manipulability of competitive equilibrium rules in many-to-many buyer–seller markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1137-1161, November.
    3. Klaus, Bettina & Klijn, Flip, 2016. "Equilibria of deferred acceptance with complete lists," Economics Letters, Elsevier, vol. 144(C), pages 98-101.
    4. Tello Benjamín, 2017. "Stability of Equilibrium Outcomes under Deferred Acceptance: Acyclicity and Dropping Strategies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 17(2), pages 1-9, June.

    More about this item

    Keywords

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    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D60 - Microeconomics - - Welfare Economics - - - General

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