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On the number of employed in the matching model

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  • Kitahara, Minoru
  • Okumura, Yasunori

Abstract

This study analyzes the number of matches in stable and efficient matchings. The benchmark number of matches is the largest one among the matchings in which no agent can be better off by itself. We show that, in the one-to-one matching model, the number of matches in any stable matching is more than or equal to the smallest integer that is not less than half of the benchmark number. This result is satisfied even if “stable matching” is replaced by “efficient matching”. We extend the model to the many-to-one matching one and provide the sets of preference profiles in which each of the above results continues to hold.

Suggested Citation

  • Kitahara, Minoru & Okumura, Yasunori, 2019. "On the number of employed in the matching model," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 63-69.
    • Handle: RePEc:eee:mateco:v:83:y:2019:i:c:p:63-69
    DOI: 10.1016/j.jmateco.2019.04.004
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    1. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
    2. Klaus, Bettina & Walzl, Markus, 2009. "Stable many-to-many matchings with contracts," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 422-434, July.
    3. Bogomolnaia, Anna & Moulin, Herve, 2015. "Size versus fairness in the assignment problem," Games and Economic Behavior, Elsevier, vol. 90(C), pages 119-127.
    4. Konishi, Hideo & Unver, M. Utku, 2006. "Credible group stability in many-to-many matching problems," Journal of Economic Theory, Elsevier, vol. 129(1), pages 57-80, July.
    5. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-627, June.
    6. Ruth Martínez & Jordi Massó & Alejdanro Neme & Jorge Oviedo, 2004. "On group strategy-proof mechanisms for a many-to-one matching model," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 115-128, January.
    7. Martínez, Ruth & Massó, Jordi & Neme, Alejandro & Oviedo, Jorge, 2010. "The Blocking Lemma for a many-to-one matching model," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 937-949, September.
    8. 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.
    9. Okumura, Yasunori, 2017. "A one-sided many-to-many matching problem," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 104-111.
    10. Lance Lochner & Enrico Moretti, 2004. "The Effect of Education on Crime: Evidence from Prison Inmates, Arrests, and Self-Reports," American Economic Review, American Economic Association, vol. 94(1), pages 155-189, March.
    11. John William Hatfield & Scott Duke Kominers & Alexander Westkamp, 2017. "Stable and Strategy-Proof Matching with Flexible Allotments," American Economic Review, American Economic Association, vol. 107(5), pages 214-219, May.
    12. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    13. Yasunori Okumura, 2019. "School Choice with General Constraints: A Market Design Approach for the Nursery School Waiting List Problem in Japan," The Japanese Economic Review, Springer, vol. 70(4), pages 497-516, December.
    14. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    15. , & ,, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    16. Heckman, James J., 2013. "Giving Kids a Fair Chance," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262019132, April.
    17. Yuichiro Kamada & Fuhito Kojima, 2015. "Efficient Matching under Distributional Constraints: Theory and Applications," American Economic Review, American Economic Association, vol. 105(1), pages 67-99, January.
    18. 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.
    19. Hatfield, John William & Kojima, Fuhito, 2009. "Group incentive compatibility for matching with contracts," Games and Economic Behavior, Elsevier, vol. 67(2), pages 745-749, November.
    20. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2000. "Single Agents and the Set of Many-to-One Stable Matchings," Journal of Economic Theory, Elsevier, vol. 91(1), pages 91-105, March.
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    Cited by:

    1. Yasunori Okumura, 2019. "School Choice with General Constraints: A Market Design Approach for the Nursery School Waiting List Problem in Japan," The Japanese Economic Review, Japanese Economic Association, vol. 70(4), pages 497-516, December.
    2. Kasajima, Yoichi & Toda, Manabu, 2024. "Singles monotonicity and stability in one-to-one matching problems," Games and Economic Behavior, Elsevier, vol. 143(C), pages 269-286.
    3. Fisher, James C.D., 2020. "Existence of stable allocations in matching markets with infinite contracts: A topological approach," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 136-140.
    4. 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.
    5. Wang, Zhihong & Li, Yangyang & Gu, Fu & Guo, Jianfeng & Wu, Xiaojun, 2020. "Two-sided matching and strategic selection on freight resource sharing platforms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    6. Yoichi Kasajima & Manabu Toda, 2021. "Singles monotonicity and stability in one-to-one matching problems," Working Papers 2023-1, Waseda University, Faculty of Political Science and Economics.

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