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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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    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.
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    5. 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.
    6. Charles Blair, 1988. "The Lattice Structure of the Set of Stable Matchings with Multiple Partners," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 619-628, November.
    7. 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.
    8. 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.
    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. Orhan Ayg?n & Tayfun S?nmez, 2013. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 103(5), pages 2050-2051, August.
    11. 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. Dimakopoulos, Philipp D. & Heller, C.-Philipp, 2019. "Matching with waiting times: The German entry-level labor market for lawyers," Games and Economic Behavior, Elsevier, vol. 115(C), pages 289-313.
    2. 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.
    3. Kominers, Scott Duke & Sönmez, Tayfun, 2016. "Matching with slot-specific priorities: theory," Theoretical Economics, Econometric Society, vol. 11(2), May.
    4. Tello, Benjamín, 2016. "Matching with contracts, substitutes and two-unit demand," Economics Letters, Elsevier, vol. 146(C), pages 85-88.
    5. 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.
    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. 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'économie 13.09, Université de Lausanne, Faculté des HEC, Département d’économie.
    8. 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.
    9. Chambers, Christopher P. & Yenmez, M. Bumin, 2018. "On lexicographic choice," Economics Letters, Elsevier, vol. 171(C), pages 222-224.
    10. Afacan, Mustafa Oǧuz, 2020. "Graduate admission with financial support," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 114-127.
    11. Philipp D. Dimakopoulos & Christian-Philipp Heller, "undated". "Matching with Waiting Times: The German Entry-Level Labour Market for Lawyers," BDPEMS Working Papers 2014005, Berlin School of Economics.
    12. M. Bumin Yenmez, 2014. "College Admissions," GSIA Working Papers 2014-E24, Carnegie Mellon University, Tepper School of Business.
    13. 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.
    14. Afacan, Mustafa Oǧuz & Turhan, Bertan, 2015. "On relationships between substitutes conditions," Economics Letters, Elsevier, vol. 126(C), pages 10-12.
    15. Aziz, Haris & Brill, Markus & Harrenstein, Paul, 2013. "Testing substitutability of weak preferences," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 91-94.
    16. Afacan, Mustafa Oǧuz, 2017. "Some further properties of the cumulative offer process," Games and Economic Behavior, Elsevier, vol. 104(C), pages 656-665.
    17. 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.
    18. Dimakopoulos, Philipp D. & Heller, C.-Philipp, 2018. "Matching with Waiting Times: The German Entry-Level Labor Market for Lawyers," Rationality and Competition Discussion Paper Series 68, CRC TRR 190 Rationality and Competition.
    19. HIRATA, Daisuke & 平田, 大祐 & KASUYA, Yusuke & 糟谷, 祐介, 2016. "Supplementary Note to “On Stable and Strategy-Proof Rules in Matching Markets with Contracts”," Discussion Papers 2016-14, Graduate School of Economics, Hitotsubashi University.

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    More about this item

    Keywords

    Matching with Contracts; Stability; Market Design;
    All these keywords.

    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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