如何最佳地销售信息：一个数学研究
How to Sell Information Optimally: an Algorithmic Study
摘要：
我们研究的算法问题出售信息的代理人面临的决策问题下的不确定性。我们采用Bergemann等人最近提出的模型。[BBS 18]，其中信息通过称为实验的信号方案揭示。在单代理设置中，任何机制都可以表示为实验菜单。我们的研究结果表明，设计收入最优菜单的计算复杂性在很大程度上取决于模型的指定方式。当所有的参数的问题是明确的，我们提供了一个多项式时间算法，计算收入最优的菜单。对于指定的模型与简洁的隐式描述的情况下，我们表明，问题的易处理性是紧密相关的最佳响应Oracle的有效实施：当它可以有效地实现，我们提供了一个添加剂的FPTAS的运行时间是独立的动作的数量。另一方面，我们提供了一个家庭的问题，它是计算上难以处理的最佳对策的预言，我们表明，这是NP-很难得到即使是一个恒定的分数的最佳收入。此外，我们研究了Bergemann等人[BBS 18]对原始模型的推广，该模型允许多个代理竞争有用的信息。我们利用拍卖设计研究中开发的技术（参见[CDW 12 a]，[AFHHM 12]，[CDW 12 b]，[CDW 13 a]，[CDW 13 b]）来设计一个多项式时间算法，该算法计算出售信息的收入最优机制。
英文摘要：
We investigate the algorithmic problem of selling information to agents who face a decision-making problem under uncertainty. We adopt the model recently proposed by Bergemann et al. [BBS18], in which information is revealed through signaling schemes called experiments. In the single-agent setting, any mechanism can be represented as a menu of experiments. Our results show that the computational complexity of designing the revenue-optimal menu depends heavily on the way the model is specified. When all the parameters of the problem are given explicitly, we provide a polynomial time algorithm that computes the revenue-optimal menu. For cases where the model is specified with a succinct implicit description, we show that the tractability of the problem is tightly related to the efficient implementation of a Best Response Oracle: when it can be implemented efficiently, we provide an additive FPTAS whose running time is independent of the number of actions. On the other hand, we provide a family of problems, where it is computationally intractable to construct a best response oracle, and we show that it is NP-hard to get even a constant fraction of the optimal revenue. Moreover, we investigate a generalization of the original model by Bergemann et al. [BBS18] that allows multiple agents to compete for useful information. We leverage techniques developed in the study of auction design (see e.g. [CDW12a], [AFHHM12], [CDW12b], [CDW13a], [CDW13b]) to design a polynomial time algorithm that computes the revenue-optimal mechanism for selling information.
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