Equilibria under deferred acceptance: Dropping strategies, filled positions, and welfare

We study many-to-one matching markets where hospitals have responsive preferences over students. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling

On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets

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, truncation strategies are exhaustive for each agent with quota 1 (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

On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets

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, truncation strategies are exhaustive for each agent with quota 1 (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

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

We consider two-sided many-to-many matching markets in which each worker maywork for multiple firms and each firmmay hire multipleworkers.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 themarket, 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). © 2013, Springer-Verlag Berlin Heidelberg.Ç. Kayi gratefully acknowledges financial support from Colciencias/CSIC (Convocatoria No: 506/2010), El Patrimonio Autónomo Fondo Nacional de Financiamiento para la Ciencia, la Tecnología y la Innovación, Francisco José de Caldas. [F. Klijn] acknowledges financial support from CSIC/Colciencias through grant 2010C00013 and the Spanish Ministry of Economy and competitiveness through Plan Nacional I+D+i (ECO2011–29847) and the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2011-0075)Peer Reviewe