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The Importance of Irrelevance of Rejected Contracts in Matching under Weakened Substitutes Conditions

Author

Listed:
  • Orhan Aygün

    () (Boston College)

  • Tayfun Sönmez

    () (Boston College)

Abstract

We show that Hatfield and Kojima (2010) inherits a critical ambiguity from its predecessor Hatfield and Milgrom (2005), and clearing this ambiguity has strong implications for the paper. Of the two potential remedies, the first one results in the failure of all theorems except one in the absence of an additional irrelevance of rejected contracts (IRC) condition, whereas the second remedy eliminates the transparency of the results, reduces the scope of the model, and contradicts authors' interpretation of the nature of their contributions. Fortunately all results are restored when IRC is explicitly assumed under the first remedy.

Suggested Citation

  • 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.
  • Handle: RePEc:boc:bocoec:805
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    File URL: http://fmwww.bc.edu/EC-P/wp805.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. Echenique, Federico, 2007. "Counting combinatorial choice rules," Games and Economic Behavior, Elsevier, vol. 58(2), pages 231-245, February.
    3. Federico Echenique, 2012. "Contracts versus Salaries in Matching," American Economic Review, American Economic Association, vol. 102(1), pages 594-601, February.
    4. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    5. 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.
    6. 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.
    7. Echenique, Federico & Oviedo, Jorge, 2004. "Core many-to-one matchings by fixed-point methods," Journal of Economic Theory, Elsevier, vol. 115(2), pages 358-376, April.
    8. 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.
    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. "Matching with Contracts: The Critical Role of Irrelevance of Rejected Contracts," Boston College Working Papers in Economics 804, Boston College Department of Economics.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Mustafa Oǧuz Afacan, 2016. "Characterizations of the cumulative offer process," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 531-542, October.
    2. Tello, Benjamín, 2016. "Matching with contracts, substitutes and two-unit demand," Economics Letters, Elsevier, vol. 146(C), pages 85-88.
    3. 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.
    4. Philipp D. Dimakopoulos & Christian-Philipp Heller, 2014. "Matching with Waiting Times: The German Entry-Level Labour Market for Lawyers," Working Papers 2014005, Berlin Doctoral Program in Economics and Management Science (BDPEMS).
    5. M. Bumin Yenmez, 2014. "College Admissions," GSIA Working Papers 2014-E24, Carnegie Mellon University, Tepper School of Business.
    6. Afacan, Mustafa Oǧuz & Turhan, Bertan, 2015. "On relationships between substitutes conditions," Economics Letters, Elsevier, vol. 126(C), pages 10-12.
    7. Aziz, Haris & Brill, Markus & Harrenstein, Paul, 2013. "Testing substitutability of weak preferences," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 91-94.
    8. repec:eee:gamebe:v:104:y:2017:i:c:p:656-665 is not listed on IDEAS
    9. 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.
    10. Kominers, Scott Duke & Sönmez, Tayfun, 2016. "Matching with slot-specific priorities: theory," Theoretical Economics, Econometric Society, vol. 11(2), May.
    11. Hirata, Daisuke & Kasuya, Yusuke, 2017. "On stable and strategy-proof rules in matching markets with contracts," Journal of Economic Theory, Elsevier, vol. 168(C), pages 27-43.
    12. 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.
    13. Jan Christoph Schlegel, 2013. "Contracts versus Salaries in Matching: Comment. N.B.: This paper is replaced by Nr 14.05 "Contracts versus Salaries in Matching: A General Result" (August 2014)," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 13.09, Université de Lausanne, Faculté des HEC, DEEP.
    14. Scott Duke Kominers & Tayfun Sönmez, 2012. "Designing for Diversity: Matching with Slot-Specific Priorities," Boston College Working Papers in Economics 806, 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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