Coherence of probabilistic constraints on Nash equilibria

Detalhes bibliográficos
Autor(a) principal: Preto, Sandro
Data de Publicação: 2022
Outros Autores: Fermé, Eduardo, Finger, Marcelo
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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spelling 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
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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
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