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. A more precise private signal about an unknown state of the world leads to an mean-preserving spread of an agent's beliefs. 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 sender-receiver persuasion games and derive sufficient conditions on the primitive payoffs that lead to extremal disclosure of information. Additionally, we study the incentives to acquire information in oligopolies when information acquisition is covert versus overt