Polyhedral Convexity and the Existence of Approximate Equilibria in Discontinuous Games
Autor(a) principal: | |
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Data de Publicação: | 2006 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10362/82985 |
Resumo: | Radzik (1991) showed that two-player games on compact intervals of the real line have ε – equilibria for all ε > 0, provided that payoff functions are upper semicontinuous and strongly quasi-concave. In an attempt to generalize this theorem, Ziad (1997) stated that the same is true for n-player games on compact, convex subsets of Rm, m ≥ 1 provided that we strengthen the upper semicontinuity condition. We show that: 1. the action spaces need to be polyhedral in order for Ziad’s approach to work, 2. Ziad’s strong upper semicontinuity condition is equivalent to some form of quasi-polyhedral concavity of players’ value functions in simple games, and 3. Radzik’s Theorem is a corollary of (the corrected) Ziad’s result. |
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Polyhedral Convexity and the Existence of Approximate Equilibria in Discontinuous GamesDiscontinuous gamesStrong upper semicontinuityStrong quasi-concavityApproximate equilibriumRadzik (1991) showed that two-player games on compact intervals of the real line have ε – equilibria for all ε > 0, provided that payoff functions are upper semicontinuous and strongly quasi-concave. In an attempt to generalize this theorem, Ziad (1997) stated that the same is true for n-player games on compact, convex subsets of Rm, m ≥ 1 provided that we strengthen the upper semicontinuity condition. We show that: 1. the action spaces need to be polyhedral in order for Ziad’s approach to work, 2. Ziad’s strong upper semicontinuity condition is equivalent to some form of quasi-polyhedral concavity of players’ value functions in simple games, and 3. Radzik’s Theorem is a corollary of (the corrected) Ziad’s result.Nova SBERUNCarmona, Guilherme2019-10-02T15:50:32Z2006-06-142006-06-14T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10362/82985engCarmona, Guilherme, Polyhedral Convexity and the Existence of Approximate Equilibria in Discontinuous Games (June, 2006). FEUNL Working Paper Series No. 488info: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:RCAAP2024-03-11T04:36:55Zoai:run.unl.pt:10362/82985Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:36:15.877635Repositório 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 |
Polyhedral Convexity and the Existence of Approximate Equilibria in Discontinuous Games |
title |
Polyhedral Convexity and the Existence of Approximate Equilibria in Discontinuous Games |
spellingShingle |
Polyhedral Convexity and the Existence of Approximate Equilibria in Discontinuous Games Carmona, Guilherme Discontinuous games Strong upper semicontinuity Strong quasi-concavity Approximate equilibrium |
title_short |
Polyhedral Convexity and the Existence of Approximate Equilibria in Discontinuous Games |
title_full |
Polyhedral Convexity and the Existence of Approximate Equilibria in Discontinuous Games |
title_fullStr |
Polyhedral Convexity and the Existence of Approximate Equilibria in Discontinuous Games |
title_full_unstemmed |
Polyhedral Convexity and the Existence of Approximate Equilibria in Discontinuous Games |
title_sort |
Polyhedral Convexity and the Existence of Approximate Equilibria in Discontinuous Games |
author |
Carmona, Guilherme |
author_facet |
Carmona, Guilherme |
author_role |
author |
dc.contributor.none.fl_str_mv |
RUN |
dc.contributor.author.fl_str_mv |
Carmona, Guilherme |
dc.subject.por.fl_str_mv |
Discontinuous games Strong upper semicontinuity Strong quasi-concavity Approximate equilibrium |
topic |
Discontinuous games Strong upper semicontinuity Strong quasi-concavity Approximate equilibrium |
description |
Radzik (1991) showed that two-player games on compact intervals of the real line have ε – equilibria for all ε > 0, provided that payoff functions are upper semicontinuous and strongly quasi-concave. In an attempt to generalize this theorem, Ziad (1997) stated that the same is true for n-player games on compact, convex subsets of Rm, m ≥ 1 provided that we strengthen the upper semicontinuity condition. We show that: 1. the action spaces need to be polyhedral in order for Ziad’s approach to work, 2. Ziad’s strong upper semicontinuity condition is equivalent to some form of quasi-polyhedral concavity of players’ value functions in simple games, and 3. Radzik’s Theorem is a corollary of (the corrected) Ziad’s result. |
publishDate |
2006 |
dc.date.none.fl_str_mv |
2006-06-14 2006-06-14T00:00:00Z 2019-10-02T15:50:32Z |
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/10362/82985 |
url |
http://hdl.handle.net/10362/82985 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Carmona, Guilherme, Polyhedral Convexity and the Existence of Approximate Equilibria in Discontinuous Games (June, 2006). FEUNL Working Paper Series No. 488 |
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 |
Nova SBE |
publisher.none.fl_str_mv |
Nova SBE |
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) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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