We extend Aumann's [3] 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, ...
We extend Aumann's [3] 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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