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Monotonicity and Nash implementation in matching markets with contracts

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  • Haake, Claus-Jochen

    (Center for Mathematical Economics, Bielefeld University)

  • Klaus, Bettina

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005), and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence (Theorem 2). In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.

Suggested Citation

  • Haake, Claus-Jochen & Klaus, Bettina, 2011. "Monotonicity and Nash implementation in matching markets with contracts," Center for Mathematical Economics Working Papers 372, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:372
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    Citations

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    Cited by:

    1. Antonio Romero-Medina & Matteo Triossi, 2023. "Take-it-or-leave-it contracts in many-to-many matching markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(2), pages 591-623, February.
    2. Doghmi, Ahmed & Ziad, Abderrahmane, 2015. "Nash implementation in private good economies with single-plateaued preferences and in matching problems," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 32-39.
    3. Bram Driesen & Andrés Perea & Hans Peters, 2010. "On Loss Aversion in Bimatrix Games," Theory and Decision, Springer, vol. 68(4), pages 367-391, April.
    4. Noelia Juarez & Paola B. Manasero & Oviedo Jorge, 2023. "Nash Implementation in a many-to-one Matching Market," Working Papers 255, Red Nacional de Investigadores en Economía (RedNIE).
    5. Alexander Westkamp, 2013. "An analysis of the German university admissions system," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 561-589, August.
    6. Claus-Jochen Haake & Bettina Klaus, 2009. "Monotonicity and Nash implementation in matching markets with contracts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(3), pages 393-410, December.
    7. Peter Chen & Michael Egesdal & Marek Pycia & M. Bumin Yenmez, 2016. "Manipulability of Stable Mechanisms," American Economic Journal: Microeconomics, American Economic Association, vol. 8(2), pages 202-214, May.
    8. Claus-Jochen Haake & Bettina Klaus, 2010. "Stability and Nash implementation in matching markets with couples," Theory and Decision, Springer, vol. 69(4), pages 537-554, October.
    9. Berden Caroline & Peters Hans, 2008. "On the Effect of Risk Aversion in Two-Person, Two-State Finance Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-18, January.
    10. Toyotaka Sakai, 2011. "A note on strategy-proofness from the doctor side in matching with contracts," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 337-342, December.
    11. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    12. Shohei Takagi & Shigehiro Serizawa, 2010. "An impossibility theorem for matching problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 245-266, July.
    13. Diss, Mostapha & Doghmi, Ahmed & Tlidi, Abdelmonaim, 2016. "Strategy proofness and unanimity in many-to-one matching markets," MPRA Paper 75927, University Library of Munich, Germany, revised 08 Dec 2016.
    14. Takashi Hayashi & Toyotaka Sakai, 2009. "Nash implementation of competitive equilibria in the job-matching market," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(4), pages 453-467, November.

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    More about this item

    Keywords

    Stability; Nash implementation; Matching with contracts; (Maskin) monotonicity;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • J41 - Labor and Demographic Economics - - Particular Labor Markets - - - Labor Contracts

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