  When selling information products, the seller can provide some free partial
information to change people's valuations so that the overall revenue can
possibly be increased. We study the general problem of advertising information
products by revealing partial information. We consider buyers who are
decision-makers. The outcomes of the decision problems depend on the state of
the world that is unknown to the buyers. The buyers can make their own
observations and thus can hold different personal beliefs about the state of
the world. There is an information seller who has access to the state of the
world. The seller can promote the information by revealing some partial
information. We assume that the seller chooses a long-term advertising strategy
and then commits to it. The seller's goal is to maximize the expected revenue.
We study the problem in two settings. (1) The seller targets buyers of a
certain type. In this case, finding the optimal advertising strategy is
equivalent to finding the concave closure of a simple function. The function is
a product of two quantities, the likelihood ratio and the cost of uncertainty.
Based on this observation, we prove some properties of the optimal mechanism,
which allow us to solve for the optimal mechanism by a finite-size convex
program. The convex program will have a polynomial-size if the state of the
world has a constant number of possible realizations or the buyers face a
decision problem with a constant number of options. For the general problem, we
prove that it is NP-hard to find the optimal mechanism. (2) When the seller
faces buyers of different types and only knows the distribution of their types,
we provide an approximation algorithm when it is not too hard to predict the
possible type of buyers who will make the purchase. For the general problem, we
prove that it is NP-hard to find a constant-factor approximation.
