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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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    References listed on IDEAS

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    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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