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On the Exhaustiveness of Truncation and Dropping Strategies in Many-to-Many Matching Markets

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  • Paula Jaramillo
  • Cagatay Kay
  • Flip Klijn

Abstract

We consider two-sided many-to-many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market.We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling).We study when truncation / dropping strategies are exhaustive for a group of agents onthe same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation / dropping strategies. We prove that for each stable mechanism, truncation strategies are exhaustive for each agent with quota (Theorem 1). We show that this result cannot be extended neither to group manipulations (even when all quotas equal 1 { Example 1), nor to individual manipulations when the agent's quota is larger than 1 (even when all other agents' quotas equal 1 { Example 2). Finally, we prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 2), i.e., independently of the quotas.

Suggested Citation

  • Paula Jaramillo & Cagatay Kay & Flip Klijn, 2012. "On the Exhaustiveness of Truncation and Dropping Strategies in Many-to-Many Matching Markets," Documentos CEDE 010316, Universidad de los Andes - CEDE.
  • Handle: RePEc:col:000089:010316
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    References listed on IDEAS

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    Cited by:

    1. Klijn, Flip & Pais, Joana & Vorsatz, Marc, 2019. "Static versus dynamic deferred acceptance in school choice: Theory and experiment," Games and Economic Behavior, Elsevier, vol. 113(C), pages 147-163.
    2. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
    3. Jaramillo, Paula & Kayı, Çaǧatay & Klijn, Flip, 2013. "Equilibria under deferred acceptance: Dropping strategies, filled positions, and welfare," Games and Economic Behavior, Elsevier, vol. 82(C), pages 693-701.

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    More about this item

    Keywords

    matching; many{to{many; stability; manipulability; truncation strategies; dropping strategies;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D60 - Microeconomics - - Welfare Economics - - - General

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