Optimal dynamic information provision

We study a dynamic model of information provision. A state of nature evolves according to a Markov chain. An advisor with commitment power decides how much information to provide to an uninformed decision maker, so as to influence his short-term decisions. We deal with a stylized class of situations, in which the decision maker has a risky action and a safe action, and the payoff to the advisor only depends on the action chosen by the decision maker. The greedy disclosure policy is the policy which, at each stage, minimizes the amount of information being disclosed in that stage, under the constraint that it maximizes the current payoff of the advisor. We prove that the greedy policy is optimal in many cases - but not always.