Nash Equilibria of Games with a Continuum of Players
Autor(a) principal: | |
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Data de Publicação: | 2004 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10362/83201 |
Resumo: | We characterize Nash equilibria of games with a continuum of players (Mas-Colell (1984)) in terms of approximate equilibria of large finite games. For the concept of (ε, ε) – equilibrium — in which the fraction of players not ε – optimizing is less than ε — we show that a strategy is a Nash equilibrium in a game with a continuum of players if and only if there exists a sequence of finite games such that its restriction is an (εn, εn) – equilibria, with εn converging to zero. The same holds for ε – equilibrium — in which almost all players are ε – optimizing — provided that either players’ payoff functions are equicontinuous or players’ action space is finite. Furthermore, we give conditions under which the above results hold for all approximating sequences of games. In our characterizations, a sequence of finite games approaches the continuum game in the sense that the number of players converges to infinity and the distribution of characteristics and actions in the finite games converges to that of the continuum game. These results render approximate equilibria of large finite economies as an alternative way of obtaining strategic insignificance. |
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Nash Equilibria of Games with a Continuum of PlayersWe characterize Nash equilibria of games with a continuum of players (Mas-Colell (1984)) in terms of approximate equilibria of large finite games. For the concept of (ε, ε) – equilibrium — in which the fraction of players not ε – optimizing is less than ε — we show that a strategy is a Nash equilibrium in a game with a continuum of players if and only if there exists a sequence of finite games such that its restriction is an (εn, εn) – equilibria, with εn converging to zero. The same holds for ε – equilibrium — in which almost all players are ε – optimizing — provided that either players’ payoff functions are equicontinuous or players’ action space is finite. Furthermore, we give conditions under which the above results hold for all approximating sequences of games. In our characterizations, a sequence of finite games approaches the continuum game in the sense that the number of players converges to infinity and the distribution of characteristics and actions in the finite games converges to that of the continuum game. These results render approximate equilibria of large finite economies as an alternative way of obtaining strategic insignificance.Nova SBERUNCarmona, Guilherme2019-10-04T09:41:28Z2004-12-212004-12-21T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10362/83201engCarmona, Guilherme, Nash Equilibria of Games with a Continuum of Players (December, 2004). FEUNL Working Paper Series No. 466info: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:RCAAP2024-03-11T04:37:06Zoai:run.unl.pt:10362/83201Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:36:17.874136Repositório 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 |
Nash Equilibria of Games with a Continuum of Players |
title |
Nash Equilibria of Games with a Continuum of Players |
spellingShingle |
Nash Equilibria of Games with a Continuum of Players Carmona, Guilherme |
title_short |
Nash Equilibria of Games with a Continuum of Players |
title_full |
Nash Equilibria of Games with a Continuum of Players |
title_fullStr |
Nash Equilibria of Games with a Continuum of Players |
title_full_unstemmed |
Nash Equilibria of Games with a Continuum of Players |
title_sort |
Nash Equilibria of Games with a Continuum of Players |
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 |
description |
We characterize Nash equilibria of games with a continuum of players (Mas-Colell (1984)) in terms of approximate equilibria of large finite games. For the concept of (ε, ε) – equilibrium — in which the fraction of players not ε – optimizing is less than ε — we show that a strategy is a Nash equilibrium in a game with a continuum of players if and only if there exists a sequence of finite games such that its restriction is an (εn, εn) – equilibria, with εn converging to zero. The same holds for ε – equilibrium — in which almost all players are ε – optimizing — provided that either players’ payoff functions are equicontinuous or players’ action space is finite. Furthermore, we give conditions under which the above results hold for all approximating sequences of games. In our characterizations, a sequence of finite games approaches the continuum game in the sense that the number of players converges to infinity and the distribution of characteristics and actions in the finite games converges to that of the continuum game. These results render approximate equilibria of large finite economies as an alternative way of obtaining strategic insignificance. |
publishDate |
2004 |
dc.date.none.fl_str_mv |
2004-12-21 2004-12-21T00:00:00Z 2019-10-04T09:41:28Z |
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/10362/83201 |
url |
http://hdl.handle.net/10362/83201 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Carmona, Guilherme, Nash Equilibria of Games with a Continuum of Players (December, 2004). FEUNL Working Paper Series No. 466 |
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info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
dc.publisher.none.fl_str_mv |
Nova SBE |
publisher.none.fl_str_mv |
Nova SBE |
dc.source.none.fl_str_mv |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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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) |
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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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