Selling less information for more: garbling with benefits Thomas A. Weber a, * , David C. Croson b a Department of Management Science and Engineering, Terman Engineering Center, Stanford University, Stanford, CA 94305-4026, USA b Department of Management Science, MIT Sloan School of Management E53-311; 30 Wadsworth Street, Cambridge, MA 02140-1830, USA Received 30 July 2002; received in revised form 8 October 2003; accepted 4 November 2003 Abstract The expected value of information in a standard portfolio investment problem with ex-post payment can increase when the information is garbled prior to its sale. Distorting the information helps to resolve the incentive problem decreasing the buyer’s default risk and thereby increasing the seller’s expected revenues. D 2004 Elsevier B.V. All rights reserved. Keywords: Value of information; Portfolio investment; Limited liability; Garbling JEL classification: C44; D81 1. Introduction In decision problems where an agent’s payoff depends on an exogenous random event, an informative signal about this event is valuable if it permits the agent to adjust her actions. The more informative the signal is in the sense of statistical sufficiency, the more valuable it is to an agent who uses it directly (Blackwell, 1953). We consider situations where an agent sells information to an investor and shows that the expected revenues from the sale may be non-monotonic in its informativeness. As an example we consider the sale of information in a simple portfolio investment problem, where the payment for the information is made after the return is realized, subject to limited liability. In the interesting case where no upfront payments for the information are permitted, we show that garbling the information (Marschak and Miyasawa, 1968) can strictly increase expected revenues for the seller by influencing the investor’s 0165-1765/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2003.11.003 * Corresponding author. Tel.: +1-650-725-6827; fax: +1-650-723-1614. E-mail address: webert@stanford.edu (T.A. Weber). www.elsevier.com/locate/econbase Economics Letters 83 (2004) 165 – 171