Approximate knowledge of rationality and correlated equilibria
AbstractWe extend Aumann's theorem [Aumann 1987], deriving correlated equilibria as a consequence of common priors and common knowledge of rationality, by explicitly allowing for non-rational behavior. We replace the assumption of common knowledge of rationality with a substantially weaker one, joint p-belief of rationality, where agents believe the other agents are rational with probability p or more. We show that behavior in this case constitutes a kind of correlated equilibrium satisfying certain p-belief constraints, and that it varies continuously in the parameters p and, for p sufficiently close to one, with high probability is supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend the analysis to characterizing rational expectations of interim types, to games of incomplete information, as well as to the case of non-common priors.
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Bibliographic InfoPaper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 1326.
Date of creation: Jun 2012
Date of revision: Oct 2012
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Web page: http://www.econ.upf.edu/
approximate common knowledge; bounded rationality; p-rational belief system; correlated equilibrium; incomplete information; non-cooperative game;
Other versions of this item:
- Fabrizio Germano & Peio Zuazo-Garin, 2012. "Approximate Knowledge of Rationality and Correlated Equilibria," Working Papers 642, Barcelona Graduate School of Economics.
- Fabrizio, Germano & Zuazo Garín, Peio, 2012. "Approximate knowledge of rationality and correlated equilibria," IKERLANAK Ikerlanak;2012-61, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
- Fabrizio Germano & Peio Zuazo-Garin, 2012. "Approximate Knowledge of Rationality and Correlated Equilibria," Discussion Paper Series dp610, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-01 (All new papers)
- NEP-GTH-2012-07-01 (Game Theory)
- NEP-KNM-2012-07-01 (Knowledge Management & Knowledge Economy)
- NEP-UPT-2012-07-01 (Utility Models & Prospect Theory)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- T. Börgers, 2010.
"Weak Dominance and Approximate Common Knowledge,"
Levine's Working Paper Archive
378, David K. Levine.
- Sergiu Hart, 2004.
Discussion Paper Series
dp372, The Center for the Study of Rationality, Hebrew University, Jerusalem.
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