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On relationships between substitutes conditions

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  • Afacan, Mustafa Oǧuz
  • Turhan, Bertan

Abstract

In the matching with contracts literature, three well-known conditions (from stronger to weaker)–substitutes, unilateral substitutes (US), and bilateral substitutes (BS)–have proven to be critical. This paper aims to deepen our understanding of them by separately axiomatizing the gap between BS and the other two. We first introduce a new “doctor separability” condition (DS) and show that BS, DS, and irrelevance of rejected contracts (IRC) are equivalent to US and IRC. Due to Hatfield and Kojima (2010) and Aygün and Sönmez (2012), we know that US, “Pareto separability” (PS), and IRC are the same as substitutes and IRC. This, along with our result, implies that BS, DS, PS, and IRC are equivalent to substitutes and IRC. All of these results are given without IRC whenever hospitals have preferences.

Suggested Citation

  • Afacan, Mustafa Oǧuz & Turhan, Bertan, 2015. "On relationships between substitutes conditions," Economics Letters, Elsevier, vol. 126(C), pages 10-12.
    • Handle: RePEc:eee:ecolet:v:126:y:2015:i:c:p:10-12
    DOI: 10.1016/j.econlet.2014.11.007
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
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    Cited by:

    1. Hirata, Daisuke & 平田, 大祐 & Kasuya, Yusuke & 糟谷, 祐介 & Okumura, Yasunori & 奥村, 保規, 2023. "Stability, Strategy-Proofness, and Respect for Improvements," Discussion Papers 2023-01, Graduate School of Economics, Hitotsubashi University.
    2. 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.
    3. 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.

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    More about this item

    Keywords

    Bilateral substitutes; Unilateral substitutes; Substitutes; Doctor separability; Pareto separability; Irrelevance of rejected contracts;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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