“Generalized Belief Operator and the Impact of Small Probability Events on Higher Order Beliefs” by Satoru Takahashi
National University of Singapore
University of Tokyo
We explore the restrictions that prior beliefs impose on higher order beliefs. We consider a generalization of belief operator, introduce a notion of potential, and study implications of existence/non-existence of a potential with a certain property. In particular, we obtain a nontrivial lower bound of the prior probability of a common belief event that is uniform over type spaces. As an application, a full characterization of robust equilibrium is obtained for binary supermodular games.