Characterizing social value of information

•The social value of information in LQG Bayesian games is characterized.•Welfare is linear in the common variance and the idiosyncratic variance of actions.•Their relative weights determine the social value of information.•If the common variance is dominant, more information always increases welfare.•If the idiosyncratic variance is dominant, more information can decrease welfare.

This paper characterizes the social value of information in Bayesian games with symmetric quadratic payoff functions and normally distributed public and private signals. The main result provides a necessary and sufficient condition for welfare to increase with public or private information. In so doing, we represent welfare as a linear combination of the variance of a common term in an equilibrium strategy and that of an idiosyncratic term, which are referred to as the common variance and the idiosyncratic variance of actions, respectively. The ratio of their coefficients is a key parameter in our condition. If the coefficient of the common variance is relatively large, welfare necessarily increases, but if it is relatively small, welfare can decrease. Using our condition, we find eight types of games with different welfare effects of information.