Random Tug-of-War games and the infinity Laplacian

In this work we introduce and analyze a new random Tug-of-War game in which one of the players has the power to decide at each turn whether to play a round of classical random Tug-of-War, or let the other player choose the new game position in exchange of a fixed payoff. We prove that this game has...

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Detalles Bibliográficos
Autor: Antón Amayuelas, Marcos
Tipo de recurso: tesis de maestría
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/106761
Acceso en línea:https://hdl.handle.net/2117/106761
Access Level:acceso abierto
Palabra clave:Differential equations, Elliptic
Infinity Laplacian
Tug-of-War
Viscosity solutions
Comparison principle
Equacions diferencials el·líptiques
Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
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spelling Random Tug-of-War games and the infinity LaplacianAntón Amayuelas, MarcosDifferential equations, EllipticInfinity LaplacianTug-of-WarViscosity solutionsComparison principleEquacions diferencials el·líptiquesClassificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic typeÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcialsIn this work we introduce and analyze a new random Tug-of-War game in which one of the players has the power to decide at each turn whether to play a round of classical random Tug-of-War, or let the other player choose the new game position in exchange of a fixed payoff. We prove that this game has a value and identify the partial differential equation to which it is related. This is the first time that such equation is found to have a relation with game theory. Moreover, our analysis relies on comparison and viscosity tools, in contrast to probabilistic arguments which are more common in the literature. The work also includes a review of the infinity Laplacian and its connection to the classical random Tug-of-War game, as well as an introduction to the theory of viscosity solutions. Furthermore, some explicit examples of the new game are considered.Universitat Politècnica de CatalunyaCharro Caballero, Fernando20172017-07-0120172017-07-24master thesishttp://purl.org/coar/resource_type/c_bdccNAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2117/106761reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1067612026-05-27T15:37:01Z
dc.title.none.fl_str_mv Random Tug-of-War games and the infinity Laplacian
title Random Tug-of-War games and the infinity Laplacian
spellingShingle Random Tug-of-War games and the infinity Laplacian
Antón Amayuelas, Marcos
Differential equations, Elliptic
Infinity Laplacian
Tug-of-War
Viscosity solutions
Comparison principle
Equacions diferencials el·líptiques
Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
title_short Random Tug-of-War games and the infinity Laplacian
title_full Random Tug-of-War games and the infinity Laplacian
title_fullStr Random Tug-of-War games and the infinity Laplacian
title_full_unstemmed Random Tug-of-War games and the infinity Laplacian
title_sort Random Tug-of-War games and the infinity Laplacian
dc.creator.none.fl_str_mv Antón Amayuelas, Marcos
author Antón Amayuelas, Marcos
author_facet Antón Amayuelas, Marcos
author_role author
dc.contributor.none.fl_str_mv Charro Caballero, Fernando
dc.subject.none.fl_str_mv Differential equations, Elliptic
Infinity Laplacian
Tug-of-War
Viscosity solutions
Comparison principle
Equacions diferencials el·líptiques
Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
topic Differential equations, Elliptic
Infinity Laplacian
Tug-of-War
Viscosity solutions
Comparison principle
Equacions diferencials el·líptiques
Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
description In this work we introduce and analyze a new random Tug-of-War game in which one of the players has the power to decide at each turn whether to play a round of classical random Tug-of-War, or let the other player choose the new game position in exchange of a fixed payoff. We prove that this game has a value and identify the partial differential equation to which it is related. This is the first time that such equation is found to have a relation with game theory. Moreover, our analysis relies on comparison and viscosity tools, in contrast to probabilistic arguments which are more common in the literature. The work also includes a review of the infinity Laplacian and its connection to the classical random Tug-of-War game, as well as an introduction to the theory of viscosity solutions. Furthermore, some explicit examples of the new game are considered.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-07-01
2017
2017-07-24
dc.type.none.fl_str_mv master thesis
http://purl.org/coar/resource_type/c_bdcc
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/106761
url https://hdl.handle.net/2117/106761
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de Catalunya
publisher.none.fl_str_mv Universitat Politècnica de Catalunya
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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