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Matching with Generalized Lexicographic Choice Rules

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  • Orhan Aygun
  • Bertan Turhan

Abstract

Motivated by the need for real-world matching problems, this paper formulates a large class of practical choice rules, Generalized Lexicographic Choice Rules (GLCR), for institutions that consist of multiple divisions. Institutions fill their divisions sequentially, and each division is endowed with a sub-choice rule that satisfies classical substitutability and size monotonicity in conjunction with a new property that we introduce, quota monotonicity. We allow rich interactions between divisions in the form of capacity transfers. The overall choice rule of an institution is defined as the union of the sub-choices of its divisions. The cumulative offer mechanism (COM) with respect to GLCR is the unique stable and strategy-proof mechanism. We define a choice-based improvement notion and show that the COM respects improvements. We employ the theory developed in this paper in our companion paper, Ayg\"un and Turhan (2020), to design satisfactory matching mechanisms for India with comprehensive affirmative action constraints.

Suggested Citation

  • Orhan Aygun & Bertan Turhan, 2020. "Matching with Generalized Lexicographic Choice Rules," Papers 2004.13261, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:2004.13261
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    References listed on IDEAS

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    1. 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.
    2. Tayfun Sönmez & M. Bumin Yenmez, 2019. "Affirmative Action in India via Vertical and Horizontal Reservations," Boston College Working Papers in Economics 977, Boston College Department of Economics.
    3. Aygün, Orhan & Turhan, Bertan, 2020. "Dynamic reserves in matching markets," Journal of Economic Theory, Elsevier, vol. 188(C).
    4. Kominers, Scott Duke & Sönmez, Tayfun, 2016. "Matching with slot-specific priorities: theory," Theoretical Economics, Econometric Society, vol. 11(2), May.
    5. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    6. Avataneo, Michelle & Turhan, Bertan, 2021. "Slot-specific priorities with capacity transfers," Games and Economic Behavior, Elsevier, vol. 129(C), pages 536-548.
    7. 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.
    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. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    11. Afacan, Mustafa Oǧuz, 2017. "Some further properties of the cumulative offer process," Games and Economic Behavior, Elsevier, vol. 104(C), pages 656-665.
    12. Orhan Aygun & Bertan Turhan, 2020. "Designing Direct Matching Mechanism for India with Comprehensive Affirmative Action," Papers 2004.13264, arXiv.org, revised Dec 2021.
    13. Alexander Westkamp, 2013. "An analysis of the German university admissions system," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 561-589, August.
    14. 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.
    15. Orhan Aygün & Bertan Turhan, 2017. "Large-Scale Affirmative Action in School Choice: Admissions to IITs in India," American Economic Review, American Economic Association, vol. 107(5), pages 210-213, May.
    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. 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.
    18. 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.
    19. Chambers, Christopher P. & Yenmez, M. Bumin, 2018. "On lexicographic choice," Economics Letters, Elsevier, vol. 171(C), pages 222-224.
    20. Orhan Ayg?n & Tayfun S?nmez, 2013. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 103(5), pages 2050-2051, August.
    21. Kojima, Fuhito & Tamura, Akihisa & Yokoo, Makoto, 2018. "Designing matching mechanisms under constraints: An approach from discrete convex analysis," Journal of Economic Theory, Elsevier, vol. 176(C), pages 803-833.
    22. Kamada, Yuichiro & Kojima, Fuhito, 2017. "Stability concepts in matching under distributional constraints," Journal of Economic Theory, Elsevier, vol. 168(C), pages 107-142.
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    1. Avataneo, Michelle & Turhan, Bertan, 2021. "Slot-specific priorities with capacity transfers," Games and Economic Behavior, Elsevier, vol. 129(C), pages 536-548.
    2. Aygün, Orhan & Turhan, Bertan, 2020. "Dynamic reserves in matching markets," Journal of Economic Theory, Elsevier, vol. 188(C).
    3. Orhan Aygun & Bertan Turhan, 2020. "Designing Direct Matching Mechanism for India with Comprehensive Affirmative Action," Papers 2004.13264, arXiv.org, revised Dec 2021.

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