Approximate Knowledge of Rationality and Correlated Equilibria
AbstractWe extend Aumann's theorem (Aumann, 1987) in 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 notion, p-belief of rationality, where agents believe the other agents are rational with probabilities p or more. We show that behavior in this case constitutes a constrained correlated equilibrium of a doubled game satisfying certain p-belief constraints and characterize the topological structure of the resulting set of p-rational outcomes. We establish continuity in the parameters p and show that, for p sufficiently close to one, the p-rational outcomes are close to the correlated equilibria and, with high probability, supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend Aumann and Dreze's theorem (Aumann and Dreze, 2008) on rational expectations of interim types to the broader p-rational belief systems, and also discuss the case of non-common priors.
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Bibliographic InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp610.
Length: 20 pages
Date of creation: Jun 2012
Date of revision:
Correlated equilibrium; approximate common knowledge; bounded rationality; p-rational belief system; common prior; information; noncooperative game;
Other versions of this item:
- 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," Economics Working Papers 1326, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 2012.
- Fabrizio Germano & Peio Zuazo-Garin, 2012. "Approximate Knowledge of Rationality and Correlated Equilibria," Working Papers 642, Barcelona Graduate School of Economics.
- 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-2012-06-25 (All new papers)
- NEP-GTH-2012-06-25 (Game Theory)
- NEP-KNM-2012-06-25 (Knowledge Management & Knowledge Economy)
- NEP-MIC-2012-06-25 (Microeconomics)
- NEP-UPT-2012-06-25 (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.:
- Sergiu Hart, 2004.
Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem
dp372, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- Borgers Tilman, 1994.
"Weak Dominance and Approximate Common Knowledge,"
Journal of Economic Theory,
Elsevier, vol. 64(1), pages 265-276, October.
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