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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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    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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