Coherence of probabilistic constraints on Nash equilibria
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.13/4985 |
Resumo: | In this work, we first deal with the modeling of game situations that reach one of possibly many Nash equilibria. Before an instance of such a game starts, an external observer does not know, a priori, what is the exact profile of actions – constituting an equilibrium – that will occur; thus, he assigns subjective probabilities to players’ actions. Such scenario is formalized as an observable game, which is a newly introduced structure for that purpose. Then, we study the decision problem of determining if a given set of probabilistic constraints assigned a priori by the observer to a given game is coherent, called the PCE-COHERENCE problem. We show several results concerning algorithms and complexity for PCE-COHERENCE when pure Nash equilibria and specific classes of games, called GNP-classes, are considered. In this context, we also study the computation of maximal and minimal probabilistic constraints on actions that preserves coherence. Finally, we study these problems when mixed Nash equilibria are allowed in GNP-classes of 2-player games. |
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Coherence of probabilistic constraints on Nash equilibriaNash equilibriumUncertain gameProbabilistic constraintsCoherence of constraints.Faculdade de Ciências Exatas e da EngenhariaIn this work, we first deal with the modeling of game situations that reach one of possibly many Nash equilibria. Before an instance of such a game starts, an external observer does not know, a priori, what is the exact profile of actions – constituting an equilibrium – that will occur; thus, he assigns subjective probabilities to players’ actions. Such scenario is formalized as an observable game, which is a newly introduced structure for that purpose. Then, we study the decision problem of determining if a given set of probabilistic constraints assigned a priori by the observer to a given game is coherent, called the PCE-COHERENCE problem. We show several results concerning algorithms and complexity for PCE-COHERENCE when pure Nash equilibria and specific classes of games, called GNP-classes, are considered. In this context, we also study the computation of maximal and minimal probabilistic constraints on actions that preserves coherence. Finally, we study these problems when mixed Nash equilibria are allowed in GNP-classes of 2-player games.Sociedade Brasileira de ComputaçãoDigitUMaPreto, SandroFermé, EduardoFinger, Marcelo2023-02-01T10:03:23Z20222022-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.13/4985engPreto, S., Fermé, E., & Finger, M. (2022). Coherence of probabilistic constraints on Nash equilibria. Journal of the Brazilian Computer Society, 28(1), 38-51.10.5753/jbcs.2022.2434info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-03-12T05:24:08Zoai:digituma.uma.pt:10400.13/4985Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T16:46:12.366834Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Coherence of probabilistic constraints on Nash equilibria |
title |
Coherence of probabilistic constraints on Nash equilibria |
spellingShingle |
Coherence of probabilistic constraints on Nash equilibria Preto, Sandro Nash equilibrium Uncertain game Probabilistic constraints Coherence of constraints . Faculdade de Ciências Exatas e da Engenharia |
title_short |
Coherence of probabilistic constraints on Nash equilibria |
title_full |
Coherence of probabilistic constraints on Nash equilibria |
title_fullStr |
Coherence of probabilistic constraints on Nash equilibria |
title_full_unstemmed |
Coherence of probabilistic constraints on Nash equilibria |
title_sort |
Coherence of probabilistic constraints on Nash equilibria |
author |
Preto, Sandro |
author_facet |
Preto, Sandro Fermé, Eduardo Finger, Marcelo |
author_role |
author |
author2 |
Fermé, Eduardo Finger, Marcelo |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
DigitUMa |
dc.contributor.author.fl_str_mv |
Preto, Sandro Fermé, Eduardo Finger, Marcelo |
dc.subject.por.fl_str_mv |
Nash equilibrium Uncertain game Probabilistic constraints Coherence of constraints . Faculdade de Ciências Exatas e da Engenharia |
topic |
Nash equilibrium Uncertain game Probabilistic constraints Coherence of constraints . Faculdade de Ciências Exatas e da Engenharia |
description |
In this work, we first deal with the modeling of game situations that reach one of possibly many Nash equilibria. Before an instance of such a game starts, an external observer does not know, a priori, what is the exact profile of actions – constituting an equilibrium – that will occur; thus, he assigns subjective probabilities to players’ actions. Such scenario is formalized as an observable game, which is a newly introduced structure for that purpose. Then, we study the decision problem of determining if a given set of probabilistic constraints assigned a priori by the observer to a given game is coherent, called the PCE-COHERENCE problem. We show several results concerning algorithms and complexity for PCE-COHERENCE when pure Nash equilibria and specific classes of games, called GNP-classes, are considered. In this context, we also study the computation of maximal and minimal probabilistic constraints on actions that preserves coherence. Finally, we study these problems when mixed Nash equilibria are allowed in GNP-classes of 2-player games. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022 2022-01-01T00:00:00Z 2023-02-01T10:03:23Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.13/4985 |
url |
http://hdl.handle.net/10400.13/4985 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Preto, S., Fermé, E., & Finger, M. (2022). Coherence of probabilistic constraints on Nash equilibria. Journal of the Brazilian Computer Society, 28(1), 38-51. 10.5753/jbcs.2022.2434 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Computação |
publisher.none.fl_str_mv |
Sociedade Brasileira de Computação |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799130933643706368 |