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On Stable and Strategy-Proof Rules in Matching Markets with Contracts

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  • HIRATA, Daisuke
  • 平田, 大祐
  • KASUYA, Yusuke
  • 糟谷, 祐介

Abstract

This paper studies stable and (one-sided) strategy-proof rules in many-to-one matching markets with contracts. Not assuming any kind of substitutes condition or the law of aggregate demand, we obtain the following results. First, the number of stable and strategy-proof rules is at most one. Second, the doctor-optimal stable rule, whenever it exists, is the unique candidate for a stable and strategy-proof rule. Third, a stable and strategy-proof rule, whenever it exists, is second-best optimal for doctor welfare, in that no individually rational and strategy-proof rule can dominate it. This last result is further generalized to non-wasteful and strategy-proof rules. Due to the weak assumptions, our analysis covers a broad range of markets, including cases where a (unique) stable and strategy-proof rule is not equal to the one induced by the cumulative offer process or the deferred acceptance algorithm.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

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  • HIRATA, Daisuke & 平田, 大祐 & KASUYA, Yusuke & 糟谷, 祐介, 2015. "On Stable and Strategy-Proof Rules in Matching Markets with Contracts," Discussion Papers 2015-10, Graduate School of Economics, Hitotsubashi University.
    • Handle: RePEc:hit:econdp:2015-10
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    References listed on IDEAS

    as
    1. Kominers, Scott Duke & Sönmez, Tayfun, 2016. "Matching with slot-specific priorities: theory," Theoretical Economics, Econometric Society, vol. 11(2), May.
    2. 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.
    3. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match," NBER Working Papers 14864, National Bureau of Economic Research, Inc.
    4. 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.
    5. Aytek Erdil, 2013. "Strategy-Proof Stochastic Assignment," Cambridge Working Papers in Economics 1333, Faculty of Economics, University of Cambridge.
    6. Parag A. Pathak & Tayfun Sönmez, 2013. "School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation," American Economic Review, American Economic Association, vol. 103(1), pages 80-106, February.
    7. Alcalde, Jose & Barbera, Salvador, 1994. "Top Dominance and the Possibility of Strategy-Proof Stable Solutions to Matching Problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 417-435, May.
    8. Anno, Hidekazu & Kurino, Morimitsu, 2016. "On the operation of multiple matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 166-185.
    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. Toyotaka Sakai, 2011. "A note on strategy-proofness from the doctor side in matching with contracts," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 337-342, December.
    11. Orhan Ayg?n & Tayfun S?nmez, 2013. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 103(5), pages 2050-2051, August.
    12. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    13. 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.
    14. Aygün, Orhan & Turhan, Bertan, 2020. "Dynamic reserves in matching markets," Journal of Economic Theory, Elsevier, vol. 188(C).
    15. Tayfun Sonmez, 1999. "Strategy-Proofness and Essentially Single-Valued Cores," Econometrica, Econometric Society, vol. 67(3), pages 677-690, May.
    16. Schlegel, Jan Christoph, 2015. "Contracts versus salaries in matching: A general result," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 552-573.
    17. Afacan, Mustafa Oǧuz & Turhan, Bertan, 2015. "On relationships between substitutes conditions," Economics Letters, Elsevier, vol. 126(C), pages 10-12.
    18. 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.
    19. Federico Echenique, 2012. "Contracts versus Salaries in Matching," American Economic Review, American Economic Association, vol. 102(1), pages 594-601, February.
    20. 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.
    21. Erdil, Aytek, 2014. "Strategy-proof stochastic assignment," Journal of Economic Theory, Elsevier, vol. 151(C), pages 146-162.
    22. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    23. Hirata, Daisuke & Kasuya, Yusuke, 2014. "Cumulative offer process is order-independent," Economics Letters, Elsevier, vol. 124(1), pages 37-40.
    24. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    25. Afacan, Mustafa Oǧuz, 2017. "Some further properties of the cumulative offer process," Games and Economic Behavior, Elsevier, vol. 104(C), pages 656-665.
    26. Peter Chen & Michael Egesdal & Marek Pycia & M. Bumin Yenmez, 2016. "Manipulability of Stable Mechanisms," American Economic Journal: Microeconomics, American Economic Association, vol. 8(2), pages 202-214, May.
    27. 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.
    28. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
    29. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
    30. Anno, Hidekazu & Kurino, Morimitsu, 2014. "Second-best incentive compatible allocation rules for multiple-type indivisible objects," Discussion Papers, Research Unit: Market Behavior SP II 2014-201, WZB Berlin Social Science Center.
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    Citations

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    Cited by:

    1. Kamada, Yuichiro & Kojima, Fuhito, 2018. "Stability and strategy-proofness for matching with constraints: a necessary and sufficient condition," Theoretical Economics, Econometric Society, vol. 13(2), May.
    2. Zhang, Jun, 2023. "Strategy-proof allocation with outside option," Games and Economic Behavior, Elsevier, vol. 137(C), pages 50-67.
    3. Schlegel, Jan Christoph, 2020. "Equivalent choice functions and stable mechanisms," Games and Economic Behavior, Elsevier, vol. 123(C), pages 41-53.
    4. 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.
    5. Avataneo, Michelle & Turhan, Bertan, 2021. "Slot-specific priorities with capacity transfers," Games and Economic Behavior, Elsevier, vol. 129(C), pages 536-548.
    6. Tayfun Sonmez & M. Bumin Yenmez, 2022. "Constitutional Implementation of Affirmative Action Policies in India," Papers 2203.01483, arXiv.org, revised Mar 2024.
    7. Kyle Greenberg & Parag A. Pathak & Tayfun Sönmez, 2024. "Redesigning the US Army's Branching Process: A Case Study in Minimalist Market Design," American Economic Review, American Economic Association, vol. 114(4), pages 1070-1106, April.
    8. Tierney, Ryan, 2022. "Incentives And Efficiency In Matching With Transfers: Towards Nonquasilinear Package Auctions," Discussion Papers on Economics 6/2022, University of Southern Denmark, Department of Economics.
    9. Alva, Samson & Manjunath, Vikram, 2019. "Strategy-proof Pareto-improvement," Journal of Economic Theory, Elsevier, vol. 181(C), pages 121-142.
    10. Ayoade, Nickesha & Pápai, Szilvia, 2023. "School choice with preference rank classes," Games and Economic Behavior, Elsevier, vol. 137(C), pages 317-341.
    11. Kyle Greenberg & Parag A. Pathak & Tayfun Sönmez, 2020. "Mechanism Design meets Priority Design: Redesigning the US Army’s Branching Process Through Market Design," Boston College Working Papers in Economics 1035, Boston College Department of Economics.
    12. Battal Dou{g}an & Kenzo Imamura & M. Bumin Yenmez, 2022. "Market Design with Deferred Acceptance: A Recipe for Policymaking," Papers 2209.06777, arXiv.org.
    13. Jan Christoph Schlegel, 2016. "Virtual Demand and Stable Mechanisms," Cahiers de Recherches Economiques du Département d'économie 16.11, Université de Lausanne, Faculté des HEC, Département d’économie.
    14. Iwase, Yusuke & Tsuruta, Shoya & Yoshimura, Akina, 2022. "Nash implementation on the basis of general priorities," Games and Economic Behavior, Elsevier, vol. 132(C), pages 368-379.
    15. Kasuya, Yusuke, 2021. "Unilateral substitutability is necessary for doctor-optimal stability," Economics Letters, Elsevier, vol. 207(C).
    16. Afacan, Mustafa Oǧuz, 2020. "Graduate admission with financial support," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 114-127.
    17. Kyle Greenberg & Parag A. Pathak & Tayfun Sonmez, 2021. "Mechanism Design meets Priority Design: Redesigning the US Army's Branching Process," Papers 2106.06582, arXiv.org.
    18. 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.
    19. Kasuya, Yusuke, 2021. "Group incentive compatibility and welfare for matching with contracts," Economics Letters, Elsevier, vol. 202(C).
    20. Yusuke Iwase, 2022. "Equivalence theorem in matching with contracts," Review of Economic Design, Springer;Society for Economic Design, vol. 26(1), pages 117-125, March.
    21. Mustafa Oğuz Afacan & Umut Dur, 2023. "Strategy‐proof size improvement: is it possible?," Scandinavian Journal of Economics, Wiley Blackwell, vol. 125(2), pages 321-338, April.
    22. Camilo J. Sirguiado & Juan Pablo Torres-Martinez, 2024. "Strategic Behavior Without Outside Options," Working Papers wp553, University of Chile, Department of Economics.

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    More about this item

    Keywords

    matching with contracts; stability; strategy-proofness; uniqueness; efficiency; irrelevance of rejected contracts;
    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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