Iterated Expectations, Compact Spaces, and Common Priors
Extending to infinite state spaces that are compact metric spaces a result previously attained by D. Samet solely in the context of finite state spaces, a necessary and suficient 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 if and only if for each random variable it is common knowledge that all Cesaro means of iterated expectations with respect to any permutation converge to the same value; this value is its expectation with respect to the common prior. It is further shown that compactness is a necessary condition for some of the results.
|Date of creation:||Oct 2009|
|Date of revision:|
|Publication status:||Published in Games and Economic Behavior, 72 (2011) 163 – 171.|
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