Template-Type: ReDIF-Paper 1.0
Author-Name: M. Ali Khan
Author-X-Name-First: M. Ali
Author-X-Name-Last: Khan
Author-Workplace-Name: Department of Economics, Johns Hopkins University, USA
Author-Name: Haomiao Yu
Author-X-Name-First: Haomiao
Author-X-Name-Last: Yu
Author-Workplace-Name: Department of Economics, Ryerson University, Canada
Author-Name: Zhixiang Zhang
Author-X-Name-First: Zhixiang 
Author-X-Name-Last: Zhang
Author-Workplace-Name: CEMA, Central University of Finance and Economics, China
Title: A Missing Equivalence Theorem on Information Structures on a General State Space
Abstract: Blackwell’s theorem on the comparison of information structures has been influential in both theoretical and applied work, but severely hampered by its confinement to finite state spaces. In the continuing use of Lebesgue density functions, authors have by and large blithely ignored this limitation. More to the point, an equivalence theorem for a general state space between one experiment being more informative than another, and being second-order dominated by its other, is constantly invoked, but is simply unavailable in the literature. In this paper, we furnish such an equivalence theorem and remove this dissonance that has dogged the subject: we do so by supplying this missing equivalence theorem, and framing it in the context of a broad selection of the antecedent (inter-disciplinary) literature. We furnish self-contained proofs in the context of a Polish observation space.
Classification-JEL: C6, D5, D8
Keywords: Information structure, sufficiency, informativeness, second-order stochastic dominance, mean-preserving spread, martingalizability, 
Length: 25 pages
Creation-Date: 2019-04
Revised-Date: 2020-06
Number: 076
File-URL: http://economics.ryerson.ca/workingpapers/wp076.pdf
File-Format: Application/pdf
Handle: RePEc:rye:wpaper:wp076