Obvious manipulations in many-to-one matching with and without contracts

Autores
Pepa Risma, Eliana Beatriz; Arribillaga, Roberto Pablo
Año de publicación
2023
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
In the two-sided many-to-one matching model with contracts, there is a bilateral market whose disjoint sides are typically referred to as doctors and hospitals. The problem consists of assigning agents from one side of the market to agents on the opposite side, through some contracts.In the studied many-to-one model, each doctor can sign one contract at most, whereas the hospitals can sign multiple contracts. Since two agents wishing to sign an existing contract are free todo it, and also the agents can unilaterally terminate previous contracts if they find it convenient,we will consider stable allocations, i.e., outcomes that are sustainable over time, supposing themarket remains unchanged.In addition to stability, the non-manipulability of a matching rule also has a central role intwo-sided matching literature. An agent manipulates a matching rule if there exists a situationin which it obtains a better result for him declaring an alternative preference to his true one.In the many-to-one matching model (with and without contracts) and substitutable preferences,any stable matching will be susceptible to manipulations. Given that manipulations can not becompletely avoided in this context we look for stable matching rules that at least prevent obviousmanipulations, as these are defined by Troyan and Morrill (2020). A manipulation is .obviousïfit is much easier for agents to recognize and execute successfully than others in a specific andformal sense.Our first result states that the D-optimal matching rule is not obviously manipulable (for doctors) in the general context of a many-to-one matching model with contracts and substitutablepreferences for hospitals. Hence, although there are no matching rules that are non-manipulableat least there is a matching rule that is non-obviously manipulable in such context. Surprisinglywe show that the opposite result holds for the H-optimal matching rule which turns out to beobviously manipulable even in the particular context of a one-to-one matching model with contracts. This result is surprising because it reveals a substantial difference between the modelswith and without contracts from the point of view of the strategic behavior of agents. Finally, we prove that the H-optimal matching rule is not obviously manipulable in the context of themany-to-one classical matching model without contracts and substitutable preferences for hospitals.
Fil: Pepa Risma, Eliana Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina
Fil: Arribillaga, Roberto Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina
XVII Congreso Dr. Antonio Monteiro
Bahía Blanca
Argentina
Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca
Materia
OBVIOUS MANIPULATIONS
MATCHING
CONTRACTS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/260933
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Obvious manipulations in many-to-one matching with and without contractsPepa Risma, Eliana BeatrizArribillaga, Roberto PabloOBVIOUS MANIPULATIONSMATCHINGCONTRACTShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In the two-sided many-to-one matching model with contracts, there is a bilateral market whose disjoint sides are typically referred to as doctors and hospitals. The problem consists of assigning agents from one side of the market to agents on the opposite side, through some contracts.In the studied many-to-one model, each doctor can sign one contract at most, whereas the hospitals can sign multiple contracts. Since two agents wishing to sign an existing contract are free todo it, and also the agents can unilaterally terminate previous contracts if they find it convenient,we will consider stable allocations, i.e., outcomes that are sustainable over time, supposing themarket remains unchanged.In addition to stability, the non-manipulability of a matching rule also has a central role intwo-sided matching literature. An agent manipulates a matching rule if there exists a situationin which it obtains a better result for him declaring an alternative preference to his true one.In the many-to-one matching model (with and without contracts) and substitutable preferences,any stable matching will be susceptible to manipulations. Given that manipulations can not becompletely avoided in this context we look for stable matching rules that at least prevent obviousmanipulations, as these are defined by Troyan and Morrill (2020). A manipulation is .obviousïfit is much easier for agents to recognize and execute successfully than others in a specific andformal sense.Our first result states that the D-optimal matching rule is not obviously manipulable (for doctors) in the general context of a many-to-one matching model with contracts and substitutablepreferences for hospitals. Hence, although there are no matching rules that are non-manipulableat least there is a matching rule that is non-obviously manipulable in such context. Surprisinglywe show that the opposite result holds for the H-optimal matching rule which turns out to beobviously manipulable even in the particular context of a one-to-one matching model with contracts. This result is surprising because it reveals a substantial difference between the modelswith and without contracts from the point of view of the strategic behavior of agents. Finally, we prove that the H-optimal matching rule is not obviously manipulable in the context of themany-to-one classical matching model without contracts and substitutable preferences for hospitals.Fil: Pepa Risma, Eliana Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; ArgentinaFil: Arribillaga, Roberto Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; ArgentinaXVII Congreso Dr. Antonio MonteiroBahía BlancaArgentinaConsejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía BlancaUniversidad Nacional del Sur2023info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjectCongresoBookhttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/260933Obvious manipulations in many-to-one matching with and without contracts; XVII Congreso Dr. Antonio Monteiro; Bahía Blanca; Argentina; 2023; 60-61CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.matematica.uns.edu.ar/xviicm/cuadernillo_xviicm_2023.pdfNacionalinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:34:54Zoai:ri.conicet.gov.ar:11336/260933instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:34:54.422CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Obvious manipulations in many-to-one matching with and without contracts
title Obvious manipulations in many-to-one matching with and without contracts
spellingShingle Obvious manipulations in many-to-one matching with and without contracts
Pepa Risma, Eliana Beatriz
OBVIOUS MANIPULATIONS
MATCHING
CONTRACTS
title_short Obvious manipulations in many-to-one matching with and without contracts
title_full Obvious manipulations in many-to-one matching with and without contracts
title_fullStr Obvious manipulations in many-to-one matching with and without contracts
title_full_unstemmed Obvious manipulations in many-to-one matching with and without contracts
title_sort Obvious manipulations in many-to-one matching with and without contracts
dc.creator.none.fl_str_mv Pepa Risma, Eliana Beatriz
Arribillaga, Roberto Pablo
author Pepa Risma, Eliana Beatriz
author_facet Pepa Risma, Eliana Beatriz
Arribillaga, Roberto Pablo
author_role author
author2 Arribillaga, Roberto Pablo
author2_role author
dc.subject.none.fl_str_mv OBVIOUS MANIPULATIONS
MATCHING
CONTRACTS
topic OBVIOUS MANIPULATIONS
MATCHING
CONTRACTS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In the two-sided many-to-one matching model with contracts, there is a bilateral market whose disjoint sides are typically referred to as doctors and hospitals. The problem consists of assigning agents from one side of the market to agents on the opposite side, through some contracts.In the studied many-to-one model, each doctor can sign one contract at most, whereas the hospitals can sign multiple contracts. Since two agents wishing to sign an existing contract are free todo it, and also the agents can unilaterally terminate previous contracts if they find it convenient,we will consider stable allocations, i.e., outcomes that are sustainable over time, supposing themarket remains unchanged.In addition to stability, the non-manipulability of a matching rule also has a central role intwo-sided matching literature. An agent manipulates a matching rule if there exists a situationin which it obtains a better result for him declaring an alternative preference to his true one.In the many-to-one matching model (with and without contracts) and substitutable preferences,any stable matching will be susceptible to manipulations. Given that manipulations can not becompletely avoided in this context we look for stable matching rules that at least prevent obviousmanipulations, as these are defined by Troyan and Morrill (2020). A manipulation is .obviousïfit is much easier for agents to recognize and execute successfully than others in a specific andformal sense.Our first result states that the D-optimal matching rule is not obviously manipulable (for doctors) in the general context of a many-to-one matching model with contracts and substitutablepreferences for hospitals. Hence, although there are no matching rules that are non-manipulableat least there is a matching rule that is non-obviously manipulable in such context. Surprisinglywe show that the opposite result holds for the H-optimal matching rule which turns out to beobviously manipulable even in the particular context of a one-to-one matching model with contracts. This result is surprising because it reveals a substantial difference between the modelswith and without contracts from the point of view of the strategic behavior of agents. Finally, we prove that the H-optimal matching rule is not obviously manipulable in the context of themany-to-one classical matching model without contracts and substitutable preferences for hospitals.
Fil: Pepa Risma, Eliana Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina
Fil: Arribillaga, Roberto Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina
XVII Congreso Dr. Antonio Monteiro
Bahía Blanca
Argentina
Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca
description In the two-sided many-to-one matching model with contracts, there is a bilateral market whose disjoint sides are typically referred to as doctors and hospitals. The problem consists of assigning agents from one side of the market to agents on the opposite side, through some contracts.In the studied many-to-one model, each doctor can sign one contract at most, whereas the hospitals can sign multiple contracts. Since two agents wishing to sign an existing contract are free todo it, and also the agents can unilaterally terminate previous contracts if they find it convenient,we will consider stable allocations, i.e., outcomes that are sustainable over time, supposing themarket remains unchanged.In addition to stability, the non-manipulability of a matching rule also has a central role intwo-sided matching literature. An agent manipulates a matching rule if there exists a situationin which it obtains a better result for him declaring an alternative preference to his true one.In the many-to-one matching model (with and without contracts) and substitutable preferences,any stable matching will be susceptible to manipulations. Given that manipulations can not becompletely avoided in this context we look for stable matching rules that at least prevent obviousmanipulations, as these are defined by Troyan and Morrill (2020). A manipulation is .obviousïfit is much easier for agents to recognize and execute successfully than others in a specific andformal sense.Our first result states that the D-optimal matching rule is not obviously manipulable (for doctors) in the general context of a many-to-one matching model with contracts and substitutablepreferences for hospitals. Hence, although there are no matching rules that are non-manipulableat least there is a matching rule that is non-obviously manipulable in such context. Surprisinglywe show that the opposite result holds for the H-optimal matching rule which turns out to beobviously manipulable even in the particular context of a one-to-one matching model with contracts. This result is surprising because it reveals a substantial difference between the modelswith and without contracts from the point of view of the strategic behavior of agents. Finally, we prove that the H-optimal matching rule is not obviously manipulable in the context of themany-to-one classical matching model without contracts and substitutable preferences for hospitals.
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/conferenceObject
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http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
status_str publishedVersion
format conferenceObject
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/260933
Obvious manipulations in many-to-one matching with and without contracts; XVII Congreso Dr. Antonio Monteiro; Bahía Blanca; Argentina; 2023; 60-61
CONICET Digital
CONICET
url http://hdl.handle.net/11336/260933
identifier_str_mv Obvious manipulations in many-to-one matching with and without contracts; XVII Congreso Dr. Antonio Monteiro; Bahía Blanca; Argentina; 2023; 60-61
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.matematica.uns.edu.ar/xviicm/cuadernillo_xviicm_2023.pdf
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eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
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dc.coverage.none.fl_str_mv Nacional
dc.publisher.none.fl_str_mv Universidad Nacional del Sur
publisher.none.fl_str_mv Universidad Nacional del Sur
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