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Matching with Slot-Specific Priorities: Theory

Author

Listed:
  • Scott Duke Kominers

    (Harvard University)

  • Tayfun Sönmez

    () (Boston College)

Abstract

We introduce a two-sided, many-to-one matching with contracts model in which agents with unit demand match to branches that may have multiple slots available to accept contracts. Each slot has its own linear priority order over contracts; a branch chooses contracts by filling its slots sequentially, according to an order of precedence. We demonstrate that in these matching markets with slot-specific priorities, branches' choice functions may not satisfy the substitutability conditions typically crucial for matching with contracts. Despite this complication, we are able to show that stable outcomes exist in this framework and can be found by a cumulative offer mechanism that is strategy-proof and respects unambiguous improvements in priority.

Suggested Citation

  • Scott Duke Kominers & Tayfun Sönmez, 2014. "Matching with Slot-Specific Priorities: Theory," Boston College Working Papers in Economics 872, Boston College Department of Economics.
  • Handle: RePEc:boc:bocoec:872
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    References listed on IDEAS

    as
    1. Kominers, Scott Duke, 2012. "On the correspondence of contracts to salaries in (many-to-many) matching," Games and Economic Behavior, Elsevier, vol. 75(2), pages 984-989.
    2. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
    3. Ehlers, Lars & Hafalir, Isa E. & Yenmez, M. Bumin & Yildirim, Muhammed A., 2014. "School choice with controlled choice constraints: Hard bounds versus soft bounds," Journal of Economic Theory, Elsevier, vol. 153(C), pages 648-683.
    4. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    5. Schlegel, Jan Christoph, 2015. "Contracts versus salaries in matching: A general result," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 552-573.
    6. 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.
    7. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    8. 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.
    9. 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.
    10. Hirata, Daisuke & Kasuya, Yusuke, 2014. "Cumulative offer process is order-independent," Economics Letters, Elsevier, vol. 124(1), pages 37-40.
    11. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2006. "Changing the Boston School Choice Mechanism," Levine's Bibliography 122247000000001022, UCLA Department of Economics.
    12. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
    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. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
    15. Hafalir, Isa Emin & Yenmez, M. Bumin & Yildirim, Muhammed Ali, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Avinatan Hassidim & Assaf Romm & Ran I. Shorrer, 2017. "Redesigning the Israeli Psychology Master's Match," American Economic Review, American Economic Association, vol. 107(5), pages 205-209, May.
    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. repec:oup:oxford:v:33:y:2017:i:4:p:541-571. is not listed on IDEAS
    4. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press, vol. 33(4), pages 541-571.
    5. Duddy, Conal, 2017. "The structure of priority in the school choice problem," MPRA Paper 81057, University Library of Munich, Germany.
    6. repec:eee:jetheo:v:176:y:2018:i:c:p:81-117 is not listed on IDEAS
    7. Schlegel, Jan Christoph, 2015. "Contracts versus salaries in matching: A general result," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 552-573.
    8. Battal Dogan & Serhat Dogan & Kemal Yildiz, 2017. "Lexicographic Choice under Variable Capacity Constraints," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 17.02, Université de Lausanne, Faculté des HEC, DEEP.
    9. repec:eee:gamebe:v:104:y:2017:i:c:p:656-665 is not listed on IDEAS
    10. repec:eee:gamebe:v:108:y:2018:i:c:p:275-286 is not listed on IDEAS
    11. Fack, Gabrielle & Grenet, Julien & He, Yinghua, 2015. "Beyond Truth-Telling: Preference Estimation with Centralized School Choice," CEPR Discussion Papers 10907, C.E.P.R. Discussion Papers.
    12. 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.
    13. repec:eee:jetheo:v:176:y:2018:i:c:p:803-833 is not listed on IDEAS
    14. 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.
    15. repec:eee:jetheo:v:171:y:2017:i:c:p:268-292 is not listed on IDEAS
    16. 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.
    17. Doğan, Battal, 2016. "Responsive affirmative action in school choice," Journal of Economic Theory, Elsevier, vol. 165(C), pages 69-105.
    18. Fragiadakis, Daniel & Troyan, Peter, 2017. "Improving matching under hard distributional constraints," Theoretical Economics, Econometric Society, vol. 12(2), May.
    19. repec:the:publsh:2717 is not listed on IDEAS
    20. repec:aea:aecrev:v:107:y:2017:i:5:p:200-204 is not listed on IDEAS
    21. repec:eee:jetheo:v:170:y:2017:i:c:p:29-55 is not listed on IDEAS
    22. Umut Mert Dur & Parag A. Pathak & Tayfun Sönmez, 2016. "Explicit vs. Statistical Preferential Treatment in Affirmative Action: Theory and Evidence from Chicago’s Exam Schools," Boston College Working Papers in Economics 906, Boston College Department of Economics.

    More about this item

    Keywords

    Market Design; Matching with Contracts; Stability; Strategy-Proofness; School Choice; Affirmative Action; Airline Seat Upgrades.;

    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
    • 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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