On the Invariance of the Set of Core Matchings with Respect to Preference Profiles

We consider the general many-to-one matching model with ordinal preferences and give a procedure to partition the set of preference profiles into subsets with the property that all preference profiles in the same subset have the same Core. We also show how to identify a profile of (incomplete) binary relations containing the minimal information needed to generate as strict extensions all the (complete) preference profiles with the same Core. This is important for applications since it reduces the amount of information that agents have to reveal about their preference relations to centralized Core matching mechanisms; moreover, this reduction is maximal.Matching, Core

On group strategy-proof mechanisms for a many-to-one matching model

For the many-to-one matching model in which firms have substitutable and quota q-separable preferences over subsets of workers we show that the workers-optimal stable mechanism is group strategy-proof for the workers. In order to prove this result, we also show that under this domain of preferences (which contains the domain of responsive preferences of the college admissions problem) the workers-optimal stable matching is weakly Pareto optimal for the workers and the Blocking Lemma holds as well. We exhibit an example showing that none of these three results remain true if the preferences of firms are substitutable but not quota q-separable.The work of R. Martínez, A. Neme, and J. Oviedo is partially supported by Research Grant 319502 from the Universidad Nacional de San Luis (Argentina). The work of J. Massó is partially supported by Research Grants BEC2002-2130 from the Dirección General de Investigación Científica y Técnica (Spanish Ministry of Science and Technology) and 2001SGR-00162 from the Departament d’Universitats, Recerca i Societat de la Informació (Generalitat de Catalunya)

Biochemical, Cellular, and Immunologic Aspects during Early Interaction between Trypanosoma cruzi and Host Cell

The close parasite-host relationship involves different aspects such as the biochemical, physiological, morphological, and immunological adaptations. Studies on parasite-host interaction have provided a myriad of information about its biology and have established the building blocks for the development of new drug therapies to control the parasite. Several mechanisms for the parasite invasion have been proposed through in vivo or in vitro experimental data. Since the first histological studies until the studies on the function/structure of the involved molecules, this complex interaction has been roughly depicted. However, new recent strategies as genetic and proteomic approaches have tuned knowledge on how the host reacts to the parasite and how the parasite avoids these host’s reactions in order to survive

The Blocking Lemma for a many-to-one maching model

We are grateful to Flip Klijn, Howard Petith, William Thomson, an associate editor, and two referees for very helpful comments. The work of R. Martínez, A. Neme and J. Oviedo is partially supported by the Universidad Nacional de San Luis, through grant 319502, and by the Consejo Nacional de Investigaciones Científicas y Técnicas CONICET, through grant PIP 112-200801-00655. Support for the research of J. Massó was received through the prize "ICREA Acadèmia" for excellence in research, funded by the Generalitat de Catalunya. He also acknowledges the support of MOVE, where he is an affiliated researcher, and of the Barcelona Graduate School of Economics (through its Research Recognition Programme), where he is an affiliated professor. His work is also supported by the Spanish Ministry of Science and Innovation, through grants ECO2008-04756 (Grupo Consolidado-C) and CONSOLIDER-INGENIO 2010 (CDS2006-00016), and by the Generalitat de Catalunya, through grant SGR2009-419. All authors acknowledge financial support from an AECI grant from the Spanish Ministry of Foreign Affairs.The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies in the fact that it has been an instrumental result to prove key results on matching. For instance, the fact that in the college admissions problem the workers-optimal stable mechanism is group strategy-proof for the workers and the strong stability theorem in the marriage model follow directly from the Blocking Lemma. However, it is known that the Blocking Lemma and its consequences do not hold in the general many-to-one matching model in which firms have substitutable preference relations. We show that the Blocking Lemma holds for the many-to-one matching model in which firms' preference relations are, in addition to substitutable, quota q-separable. We also show that the Blocking Lemma holds on a subset of substitutable preference profiles if and only if the workers-optimal stable mechanism is group strategy-proof for the workers on this subset of profile

On the lattice structure of the set of stable matchings for a many-to-one model

We thank José Alcade, Howard Petith, Alvin Roth, and a referee for their helpful comments. Financial support through a grant from the Programa de Cooperación Científica Iberoamericana is acknowledged. The work of Jordi Massó is also partially supported by Research Grants PB98-0870 from the Dirección General de Investigación Científica y Técnica, Spanish Ministry of Education and Culture, and SGR98-62 from the Comissionat per Universitats i Recerca de la Generalitat de Catalunya. The paper was partially written while Alejandro Neme was visiting the UAB under a sabbatical fellowship from the Spanish Ministry of Education and CultureFor the many-to-one matching model with firms having substitutable and q-separable preferences we propose two very natural binary operations that together with the unanimous partial ordering of the workers endow the set of stable matchings with a lattice structure. We also exhibit examples in which, under this restricted domain of firms' preferences, the classical binary operations may not even be matchin

An algorithm to compute the full set of many-to-many stable matchings

We are grateful to a referee of this journal for helpful comments and suggestions. The work of R. Martínez, A. Neme, and J. Oviedo is partially supported by Research Grant 319502 from the Universidad Nacional de San Luis (Argentina). The work of J. Massó is partially supported by the Spanish Ministry of Science and Technology, through grant BEC2002-02130, and by the Departament d'Universitats, Recerca i Societat de la Informació (Generalitat de Catalunya), through grant 2001SGR-00162 and the Barcelona Economics Program (CREA). The paper was partially written while J. Massó was visiting the Universidad Carlos III de Madrid and A. Neme was visiting the Universitat Autònoma de Barcelona. They acknowledge the hospitality of their Departments of Economics and the financial support through two sabbatical fellowships from the Departament d'Universitats, Recerca i Societat de la Informació (Generalitat de Catalunya).The paper proposes an algorithm to compute the full set of many-to-many stable matchings when agents have substitutable preferences. The algorithm starts by calculating the two optimal stable matchings using the deferred-acceptance algorithm. Then, it computes each remaining stable matching as the firm-optimal stable matching corresponding to a new preference profile, which is obtained after modifying the preferences of a previously identified sequence of firms

On the invariance of the set of Core matchings with respect to preference profiles

We are very grateful to Flip Klijn, an anonymous referee and an associate editor for their helpful comments and suggestions. We also thank participants of the Universitat Autònoma de Barcelona "Bag Lunch Workshop on Game Theory and Social Choice" and of the Duke Conference "Roth and Sotomayor: Twenty Years Later" for comments and suggestions. The work of R. Martínez, A. Neme, and J. Oviedo is partially supported by the Universidad Nacional de San Luis through grant 319502 and by the Consejo Nacional de Investigaciones Científicas y Técnicas through grant PICT-02114. Support for the research of J. Massó was received through the prize "ICREA Acadèmia" for excellence in research, funded by the Generalitat de Catalunya. He also acknowledges the support of MOVE (where he is an affiliated researcher), of the Barcelona Graduate School of Economics (where he is an affiliated professor), and of the Goverment of Catalonia, through grant SGR2009-419. His work is also supported by the Spanish Ministry of Science and Innovation through grants ECO2008-04756 (Grupo Consolidado-C) and CONSOLIDER-INGENIO 2010 (CDS2006-00016).We consider the general many-to-one matching model with ordinal preferences and give a procedure to partition the set of preference profiles into subsets with the property that all preference profiles in the same subset have the same Core. We also show how to identify a profile of (incomplete) binary relations containing the minimal information needed to generate as strict extensions all the (complete) preference profiles with the same Core. This is important for applications since it reduces the amount of information that agents have to reveal about their preference relations to centralized Core matching mechanisms; moreover, this reduction is maximal

On group strategy-proof mechanisms for a many-to-one matching model

For the many-to-one matching model in which firms have substitutable and quota q-separable preferences over subsets of workers we show that the workers-optimal stable mechanism is group strategy-proof for the workers. In order to prove this result, we also show that under this domain of preferences (which contains the domain of responsive preferences of the college admissions problem) the workers-optimal stable matching is weakly Pareto optimal for the workers and the Blocking Lemma holds as well. We exhibit an example showing that none of these three results remain true if the preferences of firms are substitutable but not quota q-separable