Another look at the Radner--Stiglitz nonconcavity in the value of information. (Q1867558)

The well-known Radner-Stiglitz theorem (RS-theorem) [\textit{R. Radner} and \textit{J. E. Stiglitz}, Stud. Bayesian Econ. 5, 33--52 (1984; Zbl 0624.90009)] gives conditions under which the marginal value of a small amount of information is zero. The above mentioned authors to present examples in which information exhibits decreasing marginal returns, so the value of information is clearly not always nonconcave. Here the RS-theorem is re-examined and extended. A particular interest was shown to the assumption of the RS-theorem of the existence of a selection from the correspondence of maximizers that is both continuous and constant in the signal realization at null information. Sufficient conditions are given separately on the information structure and the decision maker's utility function and prior beliefs to ensure the existence of such a selection. The role of these sufficient conditions is illustrated with several examples.