Selling Information While Being an Interested Party

We study the algorithmic problem faced by an information holder (seller) who wants to optimally sell information to a budged-constrained decision maker (buyer). The utilities of both agents depend on a random state of nature that is revealed to the seller, but unknown to the buyer. Differently from previous works, we consider the case in which the seller is an interested party, as the decision taken by the buyer also influences seller's utility. The seller's goal is to (partially) sell their information about the state of nature to the buyer, so as to concurrently maximize revenue and induce the buyer to take a desirable decision. We study settings in which buyer's budget and utilities are determined by a random buyer's type unknown to the seller. First, we propose a polynomial-time algorithm for computing an optimal seller's protocol, which proposes a menu of information-revelation policies to the buyer, who acquires one of them by paying its corresponding price. Then, we switch the attention to the case in which the seller can only employ a single information-revelation policy, rather than proposing a menu. In such a setting, we completely characterize the computational complexity of the seller's algorithmic problem.