Approximate knowledge of rationality and correlated equilibria
We extend Aumann's  theorem, 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 probabilities p = (pi)i?I or more. We show that behavior in this case constitutes a type 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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- Sergiu Hart, 2004.
Discussion Paper Series
dp372, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
- Sergiu Hart, 2005. "Adaptive Heuristics," Econometrica, Econometric Society, vol. 73(5), pages 1401-1430, 09.
- Sergiu Hart, 2013. "Adaptive Heuristics," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 11, pages 253-287 World Scientific Publishing Co. Pte. Ltd..
- T. Börgers, 2010.
"Weak Dominance and Approximate Common Knowledge,"
Levine's Working Paper Archive
378, David K. Levine.
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