Bayesian persuasion and its derived information design problem has been one of the main research agendas in the economics and computation literature over the past decade. However, when attempting to apply its model and theory, one is often limited by the fact that the sender can only implement very restricted information structures. Moreover, in this case, the sender can possibly achieve higher expected utility by performing a sequence of feasible experiments, where the choice of each experiment depends on the outcomes of all previous experiments. Indeed, it has been well observed that real life persuasions often take place in rounds during which the sender exhibits experiments/arguments sequentially. We study the sender's expected utility maximization using finite and infinite sequences of experiments. For infinite sequences of experiments, we characterize the supremum of the sender's expected utility using a function that generalizes the concave closure definition in the standard Bayesian persuasion problem. With this characterization, we first study a special case where the sender can use feasible experiments to achieve the optimal expected utility of the standard Bayesian persuasion without feasibility constraints, which is a trivial utility upper bound, and establish structural findings about the sender's optimal sequential design in this case. Then we derive conditions under which the sender's optimal sequential design exists; when an optimal sequential design exists, there exists an optimal design that is Markovian, i.e., the choice of the next experiment only depends on the receiver's current belief.
翻译:贝叶斯说服及其由此推导出的信息设计问题是过去十年经济学和计算机领域中的主要研究议程之一。然而,在尝试应用其模型和理论时,人们常常受制于发送方只能实施非常受限制的信息结构。此外,在这种情况下,发送方可以通过执行一系列可行实验来实现更高的期望效用,其中每次实验的选择取决于所有先前实验的结果。实际上,人们已经充分观察到,现实中的说服经常在几轮中进行,发送方依次展示一系列实验/论点。我们研究了发送方使用有限和无限的实验序列的期望效用最大化。对于无限的实验序列,我们使用一个函数来刻画发送方的期望效用的最大值,该函数推广了标准贝叶斯说服问题中的凸包定义。利用这个刻画,我们首先研究了一种特殊情况,即在不受限制的情况下通过可行实验来实现标准贝叶斯说服的最佳期望效用,这是一个微不足道的效用上限,并建立了有关发送方最优顺序设计的结构性发现在这种情况下。然后,我们推导出发送方最优顺序设计存在的条件;当存在最优顺序设计时,存在一种马尔可夫最优设计,即下一个实验的选择只取决于接收者当前信念。