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 Barcelona Graduate School of Economics in its series Working Papers with number 642.
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," Discussion Paper Series dp610, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- 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.
- 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
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- Sergiu Hart, 2005.
Econometric Society, vol. 73(5), pages 1401-1430, 09.
- 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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