Bayesian comparative statics

We study how information affects equilibria and welfare in games. For an agent, more precise information about an unknown state of the world leads to a mean-preserving spread of beliefs. We provide necessary and sufficient conditions to obtain either a non-increasing mean or a non-decreasing-mean spread of actions whenever information precision increases for at least one agent. We apply our Bayesian comparative statics framework to study informational externalities in strategic environments. In persuasion games, we derive sufficient conditions that lead to extremal disclosure of information. In oligopolistic markets, we characterize the incentives of firms to share information. In macroeconomic models, we show that information not only drives the amplitude of business cycles but also affects aggregate output.