We consider a game of persuasion with evidence between a sender and a receiver. The sender has private information. By presenting evidence on the information, the sender wishes to persuade the receiver to take a single action (e.g., hire a job candidate, or convict a defendant). The sender's utility depends solely on whether or not the receiver takes the action. The receiver's utility depends on both the action as well as the sender's private information. We study three natural variations. First, we consider sequential equilibria of the game without commitment power. Second, we consider a persuasion variant, where the sender commits to a signaling scheme and then the receiver, after seeing the evidence, takes the action or not. Third, we study a delegation variant, where the receiver first commits to taking the action if being presented certain evidence, and then the sender presents evidence to maximize the probability the action is taken. We study these variants through the computational lens, and give hardness results, optimal approximation algorithms, as well as polynomial-time algorithms for special cases. Among our results is an approximation algorithm that rounds a semidefinite program that might be of independent interest, since, to the best of our knowledge, it is the first such approximation algorithm for a natural problem in algorithmic economics.

中文翻译：

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有证据的算法说服

我们考虑发送者和接收者之间的说服游戏。发件人有私人信息。通过提供有关信息的证据，发送者希望说服接收者采取单一行动（例如，雇用求职者或将被告定罪）。发送者的效用完全取决于接收者是否采取行动。接收者的效用取决于操作以及发送者的私人信息。我们研究了三种自然变异。首先，我们考虑没有承诺力的博弈的序贯均衡。其次，我们考虑一种劝说变体，其中发送方承诺采用信号方案，然后接收方在看到证据后，是否采取行动。第三，我们研究了一个委托变体，如果收到某些证据，接收者首先承诺采取行动，然后发送者提出证据以最大化采取行动的可能性。我们通过计算镜头研究这些变体，并给出硬度结果、最佳近似算法以及特殊情况下的多项式时间算法。在我们的结果中，有一个近似算法，它可以对一个可能具有独立意义的半定程序进行舍入，因为据我们所知，它是第一个用于算法经济学中自然问题的近似算法。以及用于特殊情况的多项式时间算法。在我们的结果中，有一个近似算法，它可以对一个可能具有独立意义的半定程序进行舍入，因为据我们所知，它是第一个用于算法经济学中自然问题的近似算法。以及用于特殊情况的多项式时间算法。在我们的结果中，有一个近似算法，它可以对一个可能具有独立意义的半定程序进行舍入，因为据我们所知，它是第一个用于算法经济学中自然问题的近似算法。