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Some further properties of the cumulative offer process

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  • Afacan, Mustafa Oǧuz

Abstract

We investigate extension/resource monotonicity and respecting improvements properties of the cumulative offer process (COP). Extension monotonicity says that no doctor is to be better off whenever others start preferring more contracts to being unmatched. Resource monotonicity, on the other hand, requires that no doctor becomes worse off whenever hospitals start hiring more doctors. The COP becomes extension and resource monotonic whenever contracts are unilateral substitutes (US) satisfying an irrelevance of rejected contracts condition (IRC). This result implies that the COP is population monotonic under US and the IRC. We then turn to the respecting improvements property, which states that no doctor should be harmed if some of his contracts become more popular. With an additional law of aggregate demand condition, we show that the COP respects improvements.

Suggested Citation

  • Afacan, Mustafa Oǧuz, 2017. "Some further properties of the cumulative offer process," Games and Economic Behavior, Elsevier, vol. 104(C), pages 656-665.
    • Handle: RePEc:eee:gamebe:v:104:y:2017:i:c:p:656-665
    DOI: 10.1016/j.geb.2017.06.006
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    1. Kominers, Scott Duke & Sönmez, Tayfun, 2016. "Matching with slot-specific priorities: theory," Theoretical Economics, Econometric Society, vol. 11(2), May.
    2. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    3. Ehlers, Lars & Klaus, Bettina, 2016. "Object allocation via deferred-acceptance: Strategy-proofness and comparative statics," Games and Economic Behavior, Elsevier, vol. 97(C), pages 128-146.
    4. Fuhito Kojima & Mihai Manea, 2010. "Axioms for Deferred Acceptance," Econometrica, Econometric Society, vol. 78(2), pages 633-653, March.
    5. Federico Echenique & M. Bumin Yenmez, 2015. "How to Control Controlled School Choice," American Economic Review, American Economic Association, vol. 105(8), pages 2679-2694, August.
    6. 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.
    7. William Thomson, 1983. "The Fair Division of a Fixed Supply Among a Growing Population," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 319-326, August.
    8. Orhan Ayg?n & Tayfun S?nmez, 2013. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 103(5), pages 2050-2051, August.
    9. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    10. 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.
    11. 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.
    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. Hirata, Daisuke & Kasuya, Yusuke, 2014. "Cumulative offer process is order-independent," Economics Letters, Elsevier, vol. 124(1), pages 37-40.
    14. Chun, Youngsub & Thomson, William, 1988. "Monotonicity properties of bargaining solutions when applied to economics," Mathematical Social Sciences, Elsevier, vol. 15(1), pages 11-27, February.
    15. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    16. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
    17. Crawford, Vincent P., 1991. "Comparative statics in matching markets," Journal of Economic Theory, Elsevier, vol. 54(2), pages 389-400, August.
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    6. Aygün, Orhan & Turhan, Bertan, 2019. "Matching with Generalized Lexicographic Choice Rules," ISU General Staff Papers 20191101070000, Iowa State University, Department of Economics.
    7. Aygün, Orhan & Turhan, Bertan, 2021. "How to De-reserve Reserves," ISU General Staff Papers 202104130700001123, Iowa State University, Department of Economics.
    8. M. Bumin Yenmez, 2014. "College Admissions," GSIA Working Papers 2014-E24, Carnegie Mellon University, Tepper School of Business.
    9. 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.
    10. Tayfun Sönmez & M. Bumin Yenmez, 2019. "Constitutional Implementation of Vertical and Horizontal Reservations in India: A Unified Mechanism for Civil Service Allocation and College Admissions," Boston College Working Papers in Economics 978, Boston College Department of Economics.

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    More about this item

    Keywords

    Extension monotonicity; Resource monotonicity; Population monotonicity; Respecting improvements; The cumulative offer process; Matching with 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
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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