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Matching with Contracts: The Critical Role of Irrelevance of Rejected Contracts

Author

Listed:
  • Orhan Aygün

    () (Boston College)

  • Tayfun Sönmez

    () (Boston College)

Abstract

We show that an ambiguity in setting the primitives of the matching with contracts model by Hatfield and Milgrom (2005) has serious implications for the model. Of the two ways to clear the ambiguity, the first (and what we consider more "clean") remedy renders several of the results of the paper invalid in the absence of an additional irrelevance of removed contracts condition implicitly assumed throughout the paper, whereas the second remedy results in the lack of transparency in presentation of results while at the same time reducing the scope of the analysis with no clear benefit.

Suggested Citation

  • Orhan Aygün & Tayfun Sönmez, 2012. "Matching with Contracts: The Critical Role of Irrelevance of Rejected Contracts," Boston College Working Papers in Economics 804, Boston College Department of Economics.
  • Handle: RePEc:boc:bocoec:804
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    File URL: http://fmwww.bc.edu/EC-P/wp804.pdf
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    References listed on IDEAS

    as
    1. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
    2. Federico Echenique, 2012. "Contracts versus Salaries in Matching," American Economic Review, American Economic Association, vol. 102(1), pages 594-601, February.
    3. Tayfun Sönmez, 2013. "Bidding for Army Career Specialties: Improving the ROTC Branching Mechanism," Journal of Political Economy, University of Chicago Press, vol. 121(1), pages 186-219.
    4. Tayfun Sönmez & Tobias B. Switzer, 2011. "Matching with (Branch-of-Choice) Contracts at United States Military Academy," Boston College Working Papers in Economics 782, Boston College Department of Economics.
    5. Ahmet Alkan, 2002. "A class of multipartner matching markets with a strong lattice structure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 737-746.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Ehlers, Lars & Hafalir, Isa E. & Yenmez, M. Bumin & Yildirim, Muhammed A., 2014. "School choice with controlled choice constraints: Hard bounds versus soft bounds," Journal of Economic Theory, Elsevier, vol. 153(C), pages 648-683.
    2. Tayfun Sönmez & Tobias B. Switzer, 2013. "Matching With (Branch‐of‐Choice) Contracts at the United States Military Academy," Econometrica, Econometric Society, vol. 81(2), pages 451-488, March.
    3. Bó, Inácio, 2016. "Fair implementation of diversity in school choice," Games and Economic Behavior, Elsevier, vol. 97(C), pages 54-63.
    4. Aziz, Haris & Brill, Markus & Harrenstein, Paul, 2013. "Testing substitutability of weak preferences," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 91-94.
    5. Tayfun Sönmez, 2013. "Bidding for Army Career Specialties: Improving the ROTC Branching Mechanism," Journal of Political Economy, University of Chicago Press, vol. 121(1), pages 186-219.
    6. 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.
    7. repec:the:publsh:2717 is not listed on IDEAS
    8. Somouaoga BONKOUNGOU, 2016. "Pareto Dominance of Deferred Acceptance through Early Decision," Cahiers de recherche 11-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    9. Orhan Ayg?n & Tayfun S?nmez, 2013. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 103(5), pages 2050-2051, August.
    10. Orhan Aygün & Tayfun Sönmez, 2012. "The Importance of Irrelevance of Rejected Contracts in Matching under Weakened Substitutes Conditions," Boston College Working Papers in Economics 805, Boston College Department of Economics.

    More about this item

    Keywords

    Matching with Contracts; Stability; Market Design;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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