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.