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Equilibria of deferred acceptance with complete lists

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  • Klaus, Bettina
  • Klijn, Flip

Abstract

We study the structure of the set of (Nash) equilibria of a deferred acceptance game with complete lists: for a given marriage market with complete lists, men propose to women truthfully while women can accept or reject proposals strategically throughout the deferred-acceptance algorithm. Zhou (1991) studied this game and showed that a matching that is stable with respect to the true preferences can be supported by some preference profile (possibly a non-equilibrium one) if and only if it can be supported by an equilibrium as well. In particular, this result implies the existence of equilibria since the men-optimal stable matching is supported by true preferences and hence an equilibrium outcome. We answer an open question Zhou posed by showing that there need not exist an equilibrium matching that weakly dominates all other equilibrium matchings from the women’s point of view (Theorem 2).

Suggested Citation

  • Klaus, Bettina & Klijn, Flip, 2016. "Equilibria of deferred acceptance with complete lists," Economics Letters, Elsevier, vol. 144(C), pages 98-101.
    • Handle: RePEc:eee:ecolet:v:144:y:2016:i:c:p:98-101
    DOI: 10.1016/j.econlet.2016.04.036
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    References listed on IDEAS

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    1. Vulkan, Nir & Roth, Alvin E. & Neeman, Zvika (ed.), 2013. "The Handbook of Market Design," OUP Catalogue, Oxford University Press, number 9780199570515.
    2. Klaus, Bettina & Klijn, Flip, 2016. "Equilibria of deferred acceptance with complete lists," Economics Letters, Elsevier, vol. 144(C), pages 98-101.
    3. Roth, Alvin E & Xing, Xiaolin, 1994. "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions," American Economic Review, American Economic Association, vol. 84(4), pages 992-1044, September.
    4. Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
    5. Jaramillo, Paula & Kayı, Çaǧatay & Klijn, Flip, 2013. "Equilibria under deferred acceptance: Dropping strategies, filled positions, and welfare," Games and Economic Behavior, Elsevier, vol. 82(C), pages 693-701.
    6. 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.
    7. Chung-Piaw Teo & Jay Sethuraman & Wee-Peng Tan, 2001. "Gale-Shapley Stable Marriage Problem Revisited: Strategic Issues and Applications," Management Science, INFORMS, vol. 47(9), pages 1252-1267, September.
    8. Zhou, Lin, 1991. "Stable matchings and equilibrium outcomes of the Gale-Shapley's algorithm for the marriage problem," Economics Letters, Elsevier, vol. 36(1), pages 25-29, May.
    9. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
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    1. Klaus, Bettina & Klijn, Flip, 2016. "Equilibria of deferred acceptance with complete lists," Economics Letters, Elsevier, vol. 144(C), pages 98-101.

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    More about this item

    Keywords

    Matching; Stability; Complete lists; Nash equilibria;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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