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Matching with contracts, substitutes and two-unit demand

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  • Tello, Benjamín

Abstract

In the context of many-to-one matching with contracts, we show that for any choice function that satisfies the irrelevance of rejected contracts condition (Aygün and Sönmez, 2013) and selects at most two contracts from any given set of contracts (two-unit demand), bilateral substitutability and weak substitutability are equivalent. As a corollary, we obtain a new maximal domain for the existence of stable matchings in the unit-capacity couples model. Finally, we show with an example that the equivalence between bilateral and weak substitutability crucially depends on the two-unit demand condition.

Suggested Citation

  • Tello, Benjamín, 2016. "Matching with contracts, substitutes and two-unit demand," Economics Letters, Elsevier, vol. 146(C), pages 85-88.
    • Handle: RePEc:eee:ecolet:v:146:y:2016:i:c:p:85-88
    DOI: 10.1016/j.econlet.2016.07.016
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    References listed on IDEAS

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    1. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
    2. Bettina Klaus & Flip Klijn, 2005. "Corrigendum: Stable Matchings and Preferences of Couples," UFAE and IAE Working Papers 653.05, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    3. Parag A. Pathak & Alvin E. Roth, 2013. "Matching with Couples: Stability and Incentives in Large Markets," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(4), pages 1585-1632.
    4. Itai Ashlagi & Mark Braverman & Avinatan Hassidim, 2014. "Stability in Large Matching Markets with Complementarities," Operations Research, INFORMS, vol. 62(4), pages 713-732, August.
    5. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
    6. , Emin & , Bumin & , Ali, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
    7. Orhan Ayg?n & Tayfun S?nmez, 2013. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 103(5), pages 2050-2051, August.
    8. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    9. 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.
    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.
    11. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July.
    12. 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.
    13. Thanh Nguyen & Rakesh Vohra, 2014. "Near Feasible Stable Matchings with Complementarities," PIER Working Paper Archive 14-028, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    14. John William Hatfield & Fuhito Kojima, 2008. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 98(3), pages 1189-1194, June.
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    Cited by:

    1. Yang, Yi-You, 2020. "Rationalizable choice functions," Games and Economic Behavior, Elsevier, vol. 123(C), pages 120-126.
    2. Benjamin Tello, 2022. "Stability and Contractual Efficiency in Matching with Contracts and Lexicographic Preferences," Economics Bulletin, AccessEcon, vol. 42(1), pages 41-48.
    3. Tello, Benjamín, 2023. "Restricted complementarity and paths to stability in matching with couples," Mathematical Social Sciences, Elsevier, vol. 126(C), pages 60-67.
    4. Benjamín Tello, 2023. "Restricted Complementarity and Paths to Stability in Matching with Couples," CEMLA Working Paper Series 02/2023, CEMLA.

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    More about this item

    Keywords

    Matching; Contracts; Stability; Couples; Weak substitutability; Bilateral substitutability;
    All these keywords.

    JEL classification:

    • 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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