When selling information , sometimes the seller can increase the revenue by giving away some partial information to change the buyers'belief about the information product, so the buyers may be more willing to purchase. This work studies the general problem of advertising information products by revealing some partial information. We consider buyers who need to make a decision, the outcome of which depends on the state of the world that is unknown to the buyers.  There is an information seller who has access to the state of the world. The seller can advertise the information by revealing some partial information. We assume that the seller chooses a long-term advertising strategy and then commits to it. The buyers decide whether to purchase the full information product after seeing the partial information. The seller's goal is to maximize the expected revenue. We study the problem in two settings. 1. The seller targets the buyers of a certain type. In this case, we prove that finding the optimal advertising strategy is equivalent to finding the concave closure of a function, which is NP-hard in general . Based on this observation, we prove some properties of the optimal mechanism, which allow us to solve for the optimal mechanism by a convex program (of exponential size in general, polynomial size for special cases). We also prove some interesting characterizations of the optimal mechanisms based on these properties. 2. For the general problem when the seller faces buyers of different types and only knows the distribution of their types, it is NP-hard to find a constant factor approximation. We thus look at special cases and provide an approximation algorithm that finds an \varepsilon-suboptimal mechanism when it is not too hard to predict the possible type of buyers who will make the purchase  .
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, we prove that 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 .
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