Essays on multi-sided assignment markets

This dissertation covers the study of assignment problems in a game theoretical framework, focusing on multi-sided assignment games and stability notions. In Chapter 2, we provide some preliminaries on assignment markets and assignment games. We give some needed definitions and crucial results with...

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Autor: Atay, Ata
Tipo de recurso: tesis doctoral
Estado:Versión publicada
Fecha de publicación:2017
País:España
Institución:CBUC, CESCA
Repositorio:TDR. Tesis Doctorales en Red
OAI Identifier:oai:www.tdx.cat:10803/402148
Acceso en línea:http://hdl.handle.net/10803/402148
Access Level:acceso abierto
Palabra clave:Microeconomia
Microeconomía
Microeconomics
Teoria de jocs
Teoría de los juegos
Game theory
Jocs cooperatius (Matemàtica)
Juegos cooperativos (Matemática)
Cooperative games (Mathematics)
Ciències Jurídiques, Econòmiques i Socials
33
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repository_id_str
dc.title.none.fl_str_mv Essays on multi-sided assignment markets
title Essays on multi-sided assignment markets
spellingShingle Essays on multi-sided assignment markets
Atay, Ata
Microeconomia
Microeconomía
Microeconomics
Teoria de jocs
Teoría de los juegos
Game theory
Jocs cooperatius (Matemàtica)
Juegos cooperativos (Matemática)
Cooperative games (Mathematics)
Ciències Jurídiques, Econòmiques i Socials
33
title_short Essays on multi-sided assignment markets
title_full Essays on multi-sided assignment markets
title_fullStr Essays on multi-sided assignment markets
title_full_unstemmed Essays on multi-sided assignment markets
title_sort Essays on multi-sided assignment markets
dc.creator.none.fl_str_mv Atay, Ata
author Atay, Ata
author_facet Atay, Ata
author_role author
dc.contributor.none.fl_str_mv Núñez, Marina (Núñez Oliva)
Universitat de Barcelona. Departament de Matemàtica Econòmica, Financera i Actuarial
dc.subject.none.fl_str_mv Microeconomia
Microeconomía
Microeconomics
Teoria de jocs
Teoría de los juegos
Game theory
Jocs cooperatius (Matemàtica)
Juegos cooperativos (Matemática)
Cooperative games (Mathematics)
Ciències Jurídiques, Econòmiques i Socials
33
topic Microeconomia
Microeconomía
Microeconomics
Teoria de jocs
Teoría de los juegos
Game theory
Jocs cooperatius (Matemàtica)
Juegos cooperativos (Matemática)
Cooperative games (Mathematics)
Ciències Jurídiques, Econòmiques i Socials
33
description This dissertation covers the study of assignment problems in a game theoretical framework, focusing on multi-sided assignment games and stability notions. In Chapter 2, we provide some preliminaries on assignment markets and assignment games. We give some needed definitions and crucial results with their proof. In Chapter 3, a generalization of the classical three-sided assignment market is considered, where value is generated by pairs or triplets of agents belonging to different sectors, as well as by individuals. For these markets we represent the situation that arises when some agents leave the market with some payoff by means of a generalization of Owen (1992) derived market. Consistency with respect to the derived market, together with singleness best and individual anti-monotonicity, axiomatically characterize the core for these generalized three-sided assignment markets. When one sector is formed by buyers and the other by two different type of sellers, we show that the core coincides with the set of competitive equilibrium payoff vectors. In Chapter 4, we consider a multi-sided assignment game with the following characteristics: (a) the agents are organized in m sectors that are connected by a graph that induces a weighted m-partite graph on the set of agents, (b) a basic coalition is formed by agents from different connected sectors, and (c) the worth of a basic coalition is the addition of the weights of all its pairs that belong to connected sectors. We provide a sufficient condition on the weights to guarantee balancedness of the related multi-sided assignment game. Moreover, when the graph on the sectors is cycle-free, we prove the game is strongly balanced and the core is described by means of the cores of the underlying two-sided assignment games associated with the edges of this graph. Moreover, once selected a spanning tree of the cycle-free graph on the sectors, the equivalence between core and competitive equilibria is established. In Chapter 5, we focus on two-sided assignment games. Solymosi and Raghavan (2001) characterizes the stability of the core of the assignment game by means of a property of the valuation matrix. They show that the core of an assignment game is a von Neumann-Morgenstern stable set if and only if its valuation matrix has a dominant diagonal. Their proof makes use of some graph-theoretical tools, while the present proof relies on the notion of buyer-seller exact representative in Núñez and Rafels (2002). In Chapter 6, we study von Neumann-Morgenstern stability for three-sided assignment games. Since the core may be empty in this case, we focus on other notions of stability such as the notions of subsolution and von Neumann-Morgenstern stable sets. The dominant diagonal property is necessary for the core to be a stable set, and also sufficient in case each sector of the market has only two agents. Furthermore, for any three-sided assignment market, we prove that the union of the extended cores of all mu- compatible subgames, for a given optimal matching mu, is the core with respect to those allocations that are compatible with that matching, and it is always non-empty.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017
2017
dc.type.none.fl_str_mv info:eu-repo/semantics/doctoralThesis
info:eu-repo/semantics/publishedVersion
format doctoralThesis
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10803/402148
url http://hdl.handle.net/10803/402148
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 127 p.
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Universitat de Barcelona
publisher.none.fl_str_mv Universitat de Barcelona
dc.source.none.fl_str_mv TDX (Tesis Doctorals en Xarxa)
reponame:TDR. Tesis Doctorales en Red
instname:CBUC, CESCA
instname_str CBUC, CESCA
reponame_str TDR. Tesis Doctorales en Red
collection TDR. Tesis Doctorales en Red
repository.name.fl_str_mv
repository.mail.fl_str_mv
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spelling Essays on multi-sided assignment marketsAtay, AtaMicroeconomiaMicroeconomíaMicroeconomicsTeoria de jocsTeoría de los juegosGame theoryJocs cooperatius (Matemàtica)Juegos cooperativos (Matemática)Cooperative games (Mathematics)Ciències Jurídiques, Econòmiques i Socials33This dissertation covers the study of assignment problems in a game theoretical framework, focusing on multi-sided assignment games and stability notions. In Chapter 2, we provide some preliminaries on assignment markets and assignment games. We give some needed definitions and crucial results with their proof. In Chapter 3, a generalization of the classical three-sided assignment market is considered, where value is generated by pairs or triplets of agents belonging to different sectors, as well as by individuals. For these markets we represent the situation that arises when some agents leave the market with some payoff by means of a generalization of Owen (1992) derived market. Consistency with respect to the derived market, together with singleness best and individual anti-monotonicity, axiomatically characterize the core for these generalized three-sided assignment markets. When one sector is formed by buyers and the other by two different type of sellers, we show that the core coincides with the set of competitive equilibrium payoff vectors. In Chapter 4, we consider a multi-sided assignment game with the following characteristics: (a) the agents are organized in m sectors that are connected by a graph that induces a weighted m-partite graph on the set of agents, (b) a basic coalition is formed by agents from different connected sectors, and (c) the worth of a basic coalition is the addition of the weights of all its pairs that belong to connected sectors. We provide a sufficient condition on the weights to guarantee balancedness of the related multi-sided assignment game. Moreover, when the graph on the sectors is cycle-free, we prove the game is strongly balanced and the core is described by means of the cores of the underlying two-sided assignment games associated with the edges of this graph. Moreover, once selected a spanning tree of the cycle-free graph on the sectors, the equivalence between core and competitive equilibria is established. In Chapter 5, we focus on two-sided assignment games. Solymosi and Raghavan (2001) characterizes the stability of the core of the assignment game by means of a property of the valuation matrix. They show that the core of an assignment game is a von Neumann-Morgenstern stable set if and only if its valuation matrix has a dominant diagonal. Their proof makes use of some graph-theoretical tools, while the present proof relies on the notion of buyer-seller exact representative in Núñez and Rafels (2002). In Chapter 6, we study von Neumann-Morgenstern stability for three-sided assignment games. Since the core may be empty in this case, we focus on other notions of stability such as the notions of subsolution and von Neumann-Morgenstern stable sets. The dominant diagonal property is necessary for the core to be a stable set, and also sufficient in case each sector of the market has only two agents. Furthermore, for any three-sided assignment market, we prove that the union of the extended cores of all mu- compatible subgames, for a given optimal matching mu, is the core with respect to those allocations that are compatible with that matching, and it is always non-empty.Universitat de BarcelonaNúñez, Marina (Núñez Oliva)Universitat de Barcelona. Departament de Matemàtica Econòmica, Financera i Actuarial201720172017info:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/publishedVersion127 p.application/pdfapplication/pdfhttp://hdl.handle.net/10803/402148TDX (Tesis Doctorals en Xarxa)reponame:TDR. Tesis Doctorales en Redinstname:CBUC, CESCAInglésADVERTIMENT. L'accés als continguts d'aquesta tesi doctoral i la seva utilització ha de respectar els drets de la persona autora. Pot ser utilitzada per a consulta o estudi personal, així com en activitats o materials d'investigació i docència en els termes establerts a l'art. 32 del Text Refós de la Llei de Propietat Intel·lectual (RDL 1/1996). Per altres utilitzacions es requereix l'autorització prèvia i expressa de la persona autora. En qualsevol cas, en la utilització dels seus continguts caldrà indicar de forma clara el nom i cognoms de la persona autora i el títol de la tesi doctoral. No s'autoritza la seva reproducció o altres formes d'explotació efectuades amb finalitats de lucre ni la seva comunicació pública des d'un lloc aliè al servei TDX. Tampoc s'autoritza la presentació del seu contingut en una finestra o marc aliè a TDX (framing). Aquesta reserva de drets afecta tant als continguts de la tesi com als seus resums i índexs.info:eu-repo/semantics/openAccessoai:www.tdx.cat:10803/4021482026-06-14T12:46:07Z
score 15,300719

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