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The Blocking Lemma and strategy-proofness in many-to-many matchings

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  • Jiao, Zhenhua
  • Tian, Guoqiang

Abstract

This paper considers the incentive compatibility in many-to-many two-sided matching problems. We first show that the Blocking Lemma holds for many-to-many matchings under the extended max–min preference criterion and quota-saturability condition. This result extends the Blocking Lemma for one-to-one matching and for many-to-one matching to many-to-many matching problem. It is then shown that the deferred acceptance mechanism is strategy-proof for agents on the proposing side under the extended max–min preference criterion and quota-saturability condition. Neither the Blocking Lemma nor the incentive compatibility can be guaranteed if the preference condition is weaker than the extended max–min criterion.

Suggested Citation

  • Jiao, Zhenhua & Tian, Guoqiang, 2017. "The Blocking Lemma and strategy-proofness in many-to-many matchings," Games and Economic Behavior, Elsevier, vol. 102(C), pages 44-55.
    • Handle: RePEc:eee:gamebe:v:102:y:2017:i:c:p:44-55
    DOI: 10.1016/j.geb.2016.10.015
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    2. Antonio Romero-Medina & Matteo Triossi, 2017. "(Group) Strategy-proofness and stability in many-to many marching markets," Documentos de Trabajo 332, Centro de Economía Aplicada, Universidad de Chile.
    3. Kasuya, Yusuke, 2021. "Group incentive compatibility and welfare for matching with contracts," Economics Letters, Elsevier, vol. 202(C).

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    More about this item

    Keywords

    Many-to-many matching; Blocking Lemma; Max–min preferences; Deferred acceptance algorithm; Strategy-proofness;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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