Bayesian comparative statics

We study how changes to the informativeness of signals in Bayesian games and single-agent decision problems affect the distribution of equilibrium actions. Focusing on supermodular environments, we provide conditions under which a more precise private signal for one agent leads to an increasing-mean spread or a decreasing-mean spread of equilibrium actions for all agents. We apply our comparative statics to information disclosure games between a sender and many receivers and derive sufficient conditions on the primitive payoffs that lead to extremal disclosure of information.