Iterated Expectations and Common Priors

A necessary and sufficient condition for the existence of a common prior for several players is given in terms of the players' present beliefs only. A common prior exists iff for each random variable it is common knowledge that all its iterated expectations converge to the same value; this value is its expectation with respect to the common prior. The proof is based on the presentation of type functions as Markov matrices.Journal of Economic LiteratureClassification Numbers: C70, D82.