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

Paula Jaramillo, Çaǧatay Kayı and Flip Klijn
Authors registered in the RePEc Author Service: Çağatay Kayı

No 632, Working Papers from Barcelona School of Economics

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 on the 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, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 1), i.e., independently of the quotas. Then, we show that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 2). Finally, we show that this result cannot be extended neither to individual manipulations when the agent's quota is larger than 1 (even when all other agents' quotas equal 1 – Example 1), nor to group manipulations (even when all quotas equal 1 – Example 2).

Keywords: stability; matching; many-to-many; manipulability; truncation strategies; dropping strategies (search for similar items in EconPapers)
JEL-codes: C78 D60 (search for similar items in EconPapers)
Date: 2015-09
New Economics Papers: this item is included in nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Journal Article: On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets (2014)
Working Paper: On the Exhaustiveness of Truncation and Dropping Strategies in Many-to-Many Matching Markets (2012)
Working Paper: On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets (2012)
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