Characterizing social value of information

Abstract

This paper examines the social value of information in symmetric Bayesian games with quadratic payo↵ functions and normally distributed public and private signals. The main results identify necessary and su cient conditions for welfare to increase with public or private information. Using the conditions, we classify games into eight types by welfare e↵ects of information. In the first type, welfare necessarily increases with both public and private information.In the second type, welfare can decrease, but only with public information. In the third type, welfare can decrease as well as increase with both public and private information. In the fourth type, welfare can decrease with both, but can increase only with private information. The remaining four types are the counterparts of the above four types with the opposite welfare e↵ects of information. For each type, we characterize a socially optimal information structure and a socially optimal Bayesian correlated equilibrium.JEL classification: C72, D82.

Cournot competition and the social value of information

“…That is, 7 A full discussion of this point is relegated to the supplementary Appendix B. 8 Such perverse effects (in a perfectly-private/perfectly-public two-signal world) were documented iby Ui and Yoshizawa [46]. In an application to the Cournot setting with β = c = 0, so that π = (M + 1)/2, Ui and Yoshizawa [46, Section 4.1] reported that for M = 2 more public information is good for profits (and for welfare).…”

Bayesian Nash equilibrium and variational inequalities

“…Because of the best-response correspondence, if a potential function is strictly concave, then a Bayesian Nash equilibrium is a unique maximizer of the potential function (Ui, 2009). Basar and Ho (1974) was the first to use Radner's results to study LQG games that are not teams, followed by many studies on information sharing in oligopoly (Clark, 1983;Vives, 1984;Gal-Or, 1985) and social value of information (Morris and Shin, 2002;Angeletos and Pavan, 2007;Ui and Yoshizawa, 2015), among others. LQG games in these studies are Bayesian potential games.…”

One-leader and multiple-follower Stackelberg games with private information

“…Recent literature on information economics, following Morris and Shin (2002), includes discussions on the interrelationships between strategic behavior and public information. Angeletos and Pavan (2007) and Ui and Yoshizawa (2013) provide characterizations of those interrelationship using general Bayesian games. 1 These studies consider simultaneous-move games with uncertainty.…”

“…2 Angeletos and Pavan (2007) and Ui and Yoshizawa (2013) consider Cournot games as an industrial organization application. In another branch of the literature, Vives (1984Vives ( , 1988Vives ( , 2008Vives ( , 2011 and Myatt and Wallace (2013) analyze large Cournot games.…”