A Note on the Implications of Common Knowledge of Rationality

Abstract

I show that common knowledge of rationality is not, in general, equivalent to the limit as n → ∞ of order n mutual knowledge of rationality. In particular, one can construct games in which an action is consistent with order n mutual knowledge of rationality for every finite n but is not consistent with common knowledge of rationality. Hence finite order mutual knowledge may be very poor as an approximation of common knowledge. Journal of Economic Literature Classification Numbers: 021, 026