We study the algorithmic problem faced by an information holder (seller) who wants to optimally sell such information to a budged-constrained decision maker (buyer) that has to undertake some action. Differently from previous, we consider the case in which the seller is an interested party, as the action chosen by the buyer does not only influence their utility, but also seller's one. This happens in many real-world settings, where the way in which businesses use acquired information may positively or negatively affect the seller, due to the presence of externalities on the information market. The utilities of both the seller and the buyer depend on a random state of nature, which is revealed to the seller, but it is unknown to the buyer. Thus, 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 action. We study settings in which buyer's budget and utilities are determined by a random buyer's type that is unknown to the seller. In such settings, an optimal protocol for the seller must propose to the buyer a menu of information-revelation policies to choose from, with the latter acquiring one of them by paying its corresponding price. Moreover, since in our model the seller is an interested party, an optimal protocol must also prescribe the seller to pay back the buyer contingently on their action. First, we show that the problem of computing a seller-optimal protocol can be solved in polynomial time. Next, we switch the attention to the case in which a seller's protocol employs a single information-revelation policy, rather than proposing a menu, deriving both positive and negative results.

翻译：我们研究的是信息持有者（卖方）在希望向受预算约束的决策者（买方）最优出售信息时面临的算法问题。与以往研究不同，我们考虑了卖方作为利益相关方的情况，即买方采取的行动不仅影响自身效用，还会影响卖方效用。这一情景常见于现实场景——由于信息市场存在外部性，企业使用所购信息的方式可能对卖方产生积极或消极影响。买卖双方的效用均取决于由卖方知晓但买方未知的自然状态随机变量。因此，卖方目标是通过（部分）出售其掌握的关于自然状态的信息，同时最大化收益并引导买方采取预期行动。我们研究的场景中，买方预算和效用由卖方未知的随机买方类型决定。在此类场景中，卖方的最优协议必须向买方提供一组信息揭示策略菜单供其选择，买方通过支付对应价格获取其中一种策略。此外，由于模型中卖方是利益相关方，最优协议还需规定卖方应根据买方行为进行条件性赔付。首先，我们证明计算卖方最优协议的问题可在多项式时间内求解。接着，我们将关注点转向卖方协议仅采用单一信息揭示策略（而非提供菜单）的情形，并推导出相应的正反面结论。