Rationalizability, observability, and common knowledge
We study the strategic impact of players’ higher-order uncertainty over the observability of actions in general two-player games. More specifically, we consider the space of all belief hierarchies generated by the uncertainty over whether the game will be played as a static game or with perfect info...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10230/58742 |
| Acceso en línea: | http://hdl.handle.net/10230/58742 http://dx.doi.org/10.1093/restud/rdab047 |
| Access Level: | acceso abierto |
| Palabra clave: | Eductive co-ordination Extensive-form uncertainty First-mover advantage Kreps Hypothesis Higher-order beliefs Rationalizability Robustness Stackelberg selections |
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Rationalizability, observability, and common knowledgePenta, AntonioZuazo-Garin, PeioEductive co-ordinationExtensive-form uncertaintyFirst-mover advantageKreps HypothesisHigher-order beliefsRationalizabilityRobustnessStackelberg selectionsWe study the strategic impact of players’ higher-order uncertainty over the observability of actions in general two-player games. More specifically, we consider the space of all belief hierarchies generated by the uncertainty over whether the game will be played as a static game or with perfect information. Over this space, we characterize the correspondence of a solution concept which captures the behavioural implications of Rationality and Common Belief in Rationality (RCBR), where “rationality” is understood as sequential whenever the game is dynamic. We show that such a correspondence is generically single-valued, and that its structure supports a robust refinement of rationalizability, which often has very sharp implications. For instance, (1) in a class of games which includes both zero-sum games with a pure equilibrium and coordination games with a unique efficient equilibrium, RCBR generically ensures efficient equilibrium outcomes (eductive coordination); (2) in a class of games which also includes other well-known families of coordination games, RCBR generically selects components of the Stackelberg profiles (Stackelberg selection); (3) if it is commonly known that player ’s action is not observable (e.g. because is commonly known to move earlier, etc.), in a class of games which includes all of the above RCBR generically selects the equilibrium of the static game most favourable to player (pervasiveness of first-mover advantage).This research benefited from the support of the Spanish Ministry of Science and Innovation, PGC2018-098949-B-I00, and through the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000915-S). Antonio Penta acknowledges the financial support of the ERC Starting Grant #759424 and Peio Zuazo-Garin of the Russian Academic Excellence Project “5-100.”Oxford University Press202420242022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/58742http://dx.doi.org/10.1093/restud/rdab047reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésThe Review of Economic Studies. 2022;89(2):948-75.info:eu-repo/grantAgreement/ES/2PE/PGC2018-098949-B-I00info:eu-repo/grantAgreement/ES/2PE/CEX2019-000915-S© The Author(s) 2021. Published by Oxford University Press on behalf of The Review of Economic Studies Limited. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:10230/587422026-05-29T05:05:01Z |
| dc.title.none.fl_str_mv |
Rationalizability, observability, and common knowledge |
| title |
Rationalizability, observability, and common knowledge |
| spellingShingle |
Rationalizability, observability, and common knowledge Penta, Antonio Eductive co-ordination Extensive-form uncertainty First-mover advantage Kreps Hypothesis Higher-order beliefs Rationalizability Robustness Stackelberg selections |
| title_short |
Rationalizability, observability, and common knowledge |
| title_full |
Rationalizability, observability, and common knowledge |
| title_fullStr |
Rationalizability, observability, and common knowledge |
| title_full_unstemmed |
Rationalizability, observability, and common knowledge |
| title_sort |
Rationalizability, observability, and common knowledge |
| dc.creator.none.fl_str_mv |
Penta, Antonio Zuazo-Garin, Peio |
| author |
Penta, Antonio |
| author_facet |
Penta, Antonio Zuazo-Garin, Peio |
| author_role |
author |
| author2 |
Zuazo-Garin, Peio |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Eductive co-ordination Extensive-form uncertainty First-mover advantage Kreps Hypothesis Higher-order beliefs Rationalizability Robustness Stackelberg selections |
| topic |
Eductive co-ordination Extensive-form uncertainty First-mover advantage Kreps Hypothesis Higher-order beliefs Rationalizability Robustness Stackelberg selections |
| description |
We study the strategic impact of players’ higher-order uncertainty over the observability of actions in general two-player games. More specifically, we consider the space of all belief hierarchies generated by the uncertainty over whether the game will be played as a static game or with perfect information. Over this space, we characterize the correspondence of a solution concept which captures the behavioural implications of Rationality and Common Belief in Rationality (RCBR), where “rationality” is understood as sequential whenever the game is dynamic. We show that such a correspondence is generically single-valued, and that its structure supports a robust refinement of rationalizability, which often has very sharp implications. For instance, (1) in a class of games which includes both zero-sum games with a pure equilibrium and coordination games with a unique efficient equilibrium, RCBR generically ensures efficient equilibrium outcomes (eductive coordination); (2) in a class of games which also includes other well-known families of coordination games, RCBR generically selects components of the Stackelberg profiles (Stackelberg selection); (3) if it is commonly known that player ’s action is not observable (e.g. because is commonly known to move earlier, etc.), in a class of games which includes all of the above RCBR generically selects the equilibrium of the static game most favourable to player (pervasiveness of first-mover advantage). |
| publishDate |
2022 |
| dc.date.none.fl_str_mv |
2022 2024 2024 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
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publishedVersion |
| dc.identifier.none.fl_str_mv |
http://hdl.handle.net/10230/58742 http://dx.doi.org/10.1093/restud/rdab047 |
| url |
http://hdl.handle.net/10230/58742 http://dx.doi.org/10.1093/restud/rdab047 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
The Review of Economic Studies. 2022;89(2):948-75. info:eu-repo/grantAgreement/ES/2PE/PGC2018-098949-B-I00 info:eu-repo/grantAgreement/ES/2PE/CEX2019-000915-S |
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http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by/4.0/ |
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openAccess |
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application/pdf application/pdf |
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Oxford University Press |
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Oxford University Press |
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reponame:Recercat. Dipósit de la Recerca de Catalunya instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
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Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
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Recercat. Dipósit de la Recerca de Catalunya |
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Recercat. Dipósit de la Recerca de Catalunya |
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