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A necessary and sufficient condition for stable matching rules to be strategy-proof

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  • Takashi Akahoshi

Abstract

We study one-to-one matching problems and analyze conditions on preference domains that admit the existence of stable and strategy-proof rules. In this context, when a preference domain is unrestricted, it is known that no stable rule is strategy-proof. We introduce the notion of the no-detour condition, and show that under this condition, there is a stable and group strategy-proof rule. In addition, we show that when the men’s preference domain is unrestricted, the no-detour condition is also a necessary condition for the existence of stable and strategy-proof rules. As a result, under the assumption that the men’s preference domain is unrestricted, the following three statements are equivalent: (i) a preference domain satisfies the no-detour condition, (ii) there is a stable and group strategy-proof rule, (iii) there is a stable and strategy-proof rule. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Takashi Akahoshi, 2014. "A necessary and sufficient condition for stable matching rules to be strategy-proof," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 683-702, October.
    • Handle: RePEc:spr:sochwe:v:43:y:2014:i:3:p:683-702
    DOI: 10.1007/s00355-014-0803-1
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    Cited by:

    1. Yu Zhou & Shigehiro Serizawa, 2016. "Strategy-Proofness and Efficiency for Non-quasi-linear Common-Tiered-Object Preferences: Characterization of Minimum Price Rule," ISER Discussion Paper 0971, Institute of Social and Economic Research, Osaka University.
    2. Liu, Peng & Zeng, Huaxia, 2019. "Random assignments on preference domains with a tier structure," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 176-194.
    3. Tetsutaro Hatakeyama, 2023. "When is a sequential school choice system (non-)deficient?," Keio-IES Discussion Paper Series 2023-012, Institute for Economics Studies, Keio University.
    4. Gudmundsson , Jens, 2014. "Sequences in Pairing Problems: A New Approach to Reconcile Stability with Strategy-Proofness for Elementary Matching Problems," Working Papers 2014:40, Lund University, Department of Economics.
    5. Qiufu Chen & Yuanmei Li & Xiaopeng Yin & Luosai Zhang & Siyi Zhou, 2024. "The Machiavellian frontier of stable mechanisms," Papers 2405.12804, arXiv.org, revised Jul 2024.
    6. Zhou, Yu & Serizawa, Shigehiro, 2018. "Strategy-proofness and efficiency for non-quasi-linear and common-tiered-object preferences: Characterization of minimum price rule," Games and Economic Behavior, Elsevier, vol. 109(C), pages 327-363.

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