Optimal Advertising for Information Products
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When selling information, sometimes the seller can increase the revenue by giving away some partial information to change the buyer's belief about the information product, so the buyer may be more willing to purchase. This work studies the general problem of advertising information products by revealing some partial information. We consider a buyer who needs to make a decision, the outcome of which depends on the state of the world that is unknown to the buyer. There is an information seller who has access to information about the state of the world. The seller can advertise the information by revealing some partial information. We consider a seller who chooses an advertising strategy and then commits to it. The buyer decides whether to purchase the full information product after seeing the partial information. The seller's goal is to maximize the expected revenue. We prove that finding the optimal advertising strategy is hard, even in the simple case that the buyer type is known. Nevertheless, we show that when the buyer type is known, the problem is equivalent to finding the concave closure of a function. Based on this observation, we prove some properties of the optimal mechanism, which allow us to solve the optimal mechanism by a convex program (with exponential size in general, polynomial size for special cases). We also prove some interesting characterizations of the optimal mechanisms based on these properties. For the general problem when the seller only knows the type distribution of the buyer, it is NP-hard to find a constant factor approximation. We thus look at special cases and provide an approximation algorithm that finds an ε-suboptimal mechanism when it is not too hard to predict the possible type of buyer who will make the purchase.
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