We consider a Bayesian persuasion or information design problem where the sender tries to persuade the receiver to take a particular action via a sequence of signals. This we model by considering multi-phase trials with different experiments conducted based on the outcomes of prior experiments. In contrast to most of the literature, we consider the problem with constraints on signals imposed on the sender. This we achieve by fixing some of the experiments in an exogenous manner; these are called determined experiments. This modeling helps us understand real-world situations where this occurs: e.g., multi-phase drug trials where the FDA determines some of the experiments, funding of a startup by a venture capital firm, start-up acquisition by big firms where late-stage assessments are determined by the potential acquirer, multi-round job interviews where the candidates signal initially by presenting their qualifications but the rest of the screening procedures are determined by the interviewer. The non-determined experiments (signals) in the multi-phase trial are to be chosen by the sender in order to persuade the receiver best. With a binary state of the world, we start by deriving the optimal signaling policy in the only non-trivial configuration of a two-phase trial with binary-outcome experiments. We then generalize to multi-phase trials with binary-outcome experiments where the determined experiments can be placed at any chosen node in the trial tree. Here we present a dynamic programming algorithm to derive the optimal signaling policy that uses the two-phase trial solution's structural insights. We also contrast the optimal signaling policy structure with classical Bayesian persuasion strategies to highlight the impact of the signaling constraints on the sender.
翻译:我们考虑的是巴耶斯说服或信息设计问题,即发送者试图通过信号序列说服接收者采取特定行动的多阶段性药物试验。我们通过考虑多阶段性试验,根据先前实验的结果进行不同的实验来模拟。与大多数文献相比,我们考虑的问题是对发送者信号施加的限制。我们通过用外源方式修补一些实验来实现这一点;这些称为确定实验。这种模型有助于我们理解发生这种情况的实际情况:例如,多阶段性药物试验,即林业发展局决定一些实验的多阶段性药物试验,由一家风险资本公司供资启动,由大公司启动,由大公司购买,由潜在获取者决定末期评估,多阶段性工作面试,候选人首先通过展示其资质,而其余的筛选程序则由访谈者决定。多阶段试验中未确定的实验(信号)将由发送者选择,以便说服接收者最佳的。随着世界的二进制状态,我们开始在仅由非三阶段性信号性结构性指标性分析中提出最佳的信号政策性政策购买,然后是两阶段性试验,我们确定两个阶段性试验中的任何最佳性试验。我们先期试验可以选择。我们先先先在两个阶段性试验阶段性试验阶段性试验阶段性试验阶段性试验阶段性试验阶段性试验阶段性试验阶段性试验中确定最佳的周期性试验。