Comparison of Information Structures with Infinite States of Nature

(Abstract)

Blackwell's theorem has been extensively employed in the decision theory involving information and uncertainty. However, the potential application has been hampered by its assumption of a finite number of states of nature. In this paper we establish the results of Blackwell theorem with general states of nature. The idea behind the generalization is to approximate an infinite case with finite ones through proper limiting arguments. We show, under some mild conditions, the equivalence between increased informativeness, sufficiency and mean-preserving spread of the a priori estimated distribution of the posterior distributions.