Iterated Expectations with Common Beliefs

This paper generalizes a result by Samet concerning iterated expecta- tions and common priors. When a player in some state of the world is allowed to ascribe probability zero to that state, something not allowed in Samet s framework, iterated expectations may not converge, and when they do, common knowledge of their limit may not characterize a common prior. It is shown here that replacing common knowledge with common belief, convergence is still lost in general, but when it obtains, the full characterization is restored.