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Stability and Contractual Efficiency in Matching with Contracts and Lexicographic Preferences

Author

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  • Benjamin Tello

    (Centro de Estudios Monetarios Latinoamericanos)

Abstract

We introduce an efficiency concept in matching markets with contracts called contractual efficiency. Contractual efficiency requires that each student is assigned to a school under her most preferred contractual term. We show that while in general it is not possible to have stable and contractually efficient matchings; if the preferences of each school are lexicographic, then there is a contractually efficient and stable matching. Moreover, we provided an algorithm, the Best-Term Deferred Acceptance (Best-Term DA) algorithm, that produces a contractually efficient and stable matching whenever schools' preferences are lexicographic. Finally, we turn to the question of whether a contractually efficient and stable matching can be implemented in dominant strategies. We show that in a two-stage matching market whereby contractual terms can be interpreted as pre-matching investments -each student first chooses her investment and then students and schools match according to the School-Optimal Stable Matching-, it is a dominant strategy for each student to choose the investment associated with the outcome of the Best-Term DA algorithm and the outcome of the two-stage market is precisely the outcome of the Best-Term DA algorithm.

Suggested Citation

  • Benjamin Tello, 2022. "Stability and Contractual Efficiency in Matching with Contracts and Lexicographic Preferences," Economics Bulletin, AccessEcon, vol. 42(1), pages 41-48.
    • Handle: RePEc:ebl:ecbull:eb-21-01076
    as

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    References listed on IDEAS

    as
    1. Caterina Calsamiglia & Guillaume Haeringer & Flip Klijn, 2010. "Constrained School Choice: An Experimental Study," American Economic Review, American Economic Association, vol. 100(4), pages 1860-1874, September.
    2. Tello, Benjamín, 2016. "Matching with contracts, substitutes and two-unit demand," Economics Letters, Elsevier, vol. 146(C), pages 85-88.
    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. 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.
    5. 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.
    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. 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.
    8. Tamás Fleiner, 2003. "A Fixed-Point Approach to Stable Matchings and Some Applications," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 103-126, February.
    9. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
    10. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
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    More about this item

    Keywords

    matching; stability; contractual efficiency; lexicographic preferences;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D6 - Microeconomics - - Welfare Economics

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