An updating rule specifies how an agent reacts to information. An updating rule is Blackwell monotone if more information is always better for an agent in a decision problem and strictly Blackwell monotone if, in addition, there is always a decision problem in which more information is strictly better for an agent. Bayes'law is strictly Blackwell monotone, and I show that within a broad class of updating rules--those that distort the Bayesian posteriors in a signal-independent manner--it is the only strictly Blackwell-monotone updating rule. If an agent's decisions are evaluated non-paternalistically (according to her beliefs), the Blackwell-monotone updating rules are affine distortions of the Bayesian posteriors.

We study what changes to an agent's decision problem increase her value for information. We prove that information becomes more valuable if and only if the agent's reduced-form payoff in her belief becomes more convex. When the transformation corresponds to the addition of an action, the requisite increase in convexity occurs if and only if a simple geometric condition holds, which extends in a natural way to the addition of multiple actions. We apply these findings to two scenarios: a monopolistic screening problem in which the good is information and delegation with information acquisition.

We consider a model of oligopolistic competition in a market with search frictions, in which competing firms with products of unknown quality advertise how much information a consumer’s visit will glean. In the unique symmetric equilibrium of this game, the countervailing incentives of attraction and persuasion yield a payoff function for each firm that is linear in the firm’s realized effective value. If the expected quality of the products is sufficiently high (or competition is sufficiently fierce), this corresponds to full information: firms provide the first-best level of information. If not, this corresponds to information dispersion: firms randomize over signals.