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Nash implementation of constrained efficient stable matchings under weak priorities

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  • Kumano, Taro

Abstract

In this study, we consider priority-based matching problems in which indifferent priorities are allowed. Although indifferences in priorities are naturally present in practice, it is unknown whether constrained efficient stable matchings are implementable in any strategic solution concept. Therefore, in this study, we show that (1) stable matchings are Nash implementable via a “practical” mechanism and (2) constrained efficient stable matchings are Nash implementable if and only if priorities satisfy the conditions identified by Ehlers and Erdil (2010). These findings immediately imply that efficient and stable matchings are Nash implementable under the same condition.

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  • Kumano, Taro, 2017. "Nash implementation of constrained efficient stable matchings under weak priorities," Games and Economic Behavior, Elsevier, vol. 104(C), pages 230-240.
    • Handle: RePEc:eee:gamebe:v:104:y:2017:i:c:p:230-240
    DOI: 10.1016/j.geb.2017.04.003
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    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. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    3. Saijo, Tatsuyoshi, 1988. "Strategy Space Reduction in Maskin's Theorem: Sufficient Conditions for Nash Implementation," Econometrica, Econometric Society, vol. 56(3), pages 693-700, May.
    4. Ergin, Haluk & Sonmez, Tayfun, 2006. "Games of school choice under the Boston mechanism," Journal of Public Economics, Elsevier, vol. 90(1-2), pages 215-237, January.
    5. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
    6. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
    7. Sonmez, Tayfun, 1996. "Implementation in generalized matching problems," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 429-439.
    8. 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.
    9. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 197-218.
    10. 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.
    11. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-1099, September.
    12. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, vol. 98(3), pages 669-689, June.
    13. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, vol. 64(1), pages 51-67, September.
    14. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
    15. Ehlers, Lars & Erdil, Aytek, 2010. "Efficient assignment respecting priorities," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1269-1282, May.
    16. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
    17. Kara, Tarik & Sonmez, Tayfun, 1996. "Nash Implementation of Matching Rules," Journal of Economic Theory, Elsevier, vol. 68(2), pages 425-439, February.
    18. Fuhito Kojima, 2008. "Games of school choice under the Boston mechanism with general priority structures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(3), pages 357-365, October.
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    2. 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.
    3. Minoru Kitahara & Yasunori Okumura, 2021. "Improving efficiency in school choice under partial priorities," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 971-987, December.

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    More about this item

    Keywords

    Matching; Stability; Efficiency; Nash implementation; Indifferences;
    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
    • 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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