Journal of Economic Theory 137 (2007) 696 – 708 www.elsevier.com/locate/jet Notes, Comments, and Letters to the Editor A tight sufficient condition for Radner–Stiglitz nonconcavity in the value of information Michel De Lara a , ∗ , Laurent Gilotte b, 1 a CERMICS, École des ponts, Paris Tech, 77455 Marne laVallée Cedex 2, France b CIRED, 94736 Nogent-sur-Marne Cedex, France Received 14 January 2005; final version received 21 January 2007 Available online 28 March 2007 Abstract This paper deals with the existence of a nonconcavity in the value of information, as was first explained by Radner and Stiglitz [A nonconcavity in the value of information, in: M. Boyer, R.E. Kihlstrom (Eds.), Bayesian Models in Economic Theory, Elsevier Science Publishers, Amsterdam, 1984, pp. 33–52 (Chapter 3)]. After defining infinitesimal information distance variation IIDV, we find that IIDV = 0 is sufficient for a zero marginal value of information at the null. This is a condition only on the information structure and in particular is independent of the decision maker’s preferences. This condition is tight: when IIDV > 0, there exists a payoff function for which the marginal value of information at the null is positive under general assumptions. © 2007 Published by Elsevier Inc. JEL classification: D830 Keywords: Value of information; Marginal value of information at the null; Radner–Stiglitz nonconcavity 1. Introduction This paper reexamines sufficient conditions for the Radner–Stiglitz nonconcavity of the value of information to a single decision maker. The basic problem is the classic one in which the decision maker chooses an action under uncertainty about a payoff-relevant state of the world. The decision maker has some prior beliefs over possible states and may also observe a realized signal from an information structure. The decision maker chooses a decision rule mapping realized signals ∗ Corresponding author. Fax: +33 164153586. E-mail addresses: delara@cermics.enpc.fr (M. De Lara), gilotte@centre-cired.fr (L. Gilotte). 1 Present address: EDF R&D, B.P. 408, 92141 Clamart Cedex, France. 0022-0531/$ - see front matter © 2007 Published by Elsevier Inc. doi:10.1016/j.jet.2007.01.014