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：贝叶斯说服及其衍生的信息设计问题在过去十年间一直是经济学与计算领域的主要研究议题之一。然而，在尝试应用其模型与理论时，人们往往受限于发送者只能实施极为受限的信息结构这一事实。此外，在这种情况下，发送者可以通过执行一系列可行实验来获得更高的期望效用，其中每个实验的选择取决于所有先前实验的结果。事实上，现实生活中的说服行为常以轮次形式展开，其间发送者会序贯地展示实验/论据，这一点已得到充分观察。我们研究了发送者使用有限序列及无限序列实验时的期望效用最大化问题。对于无限序列实验，我们通过一个泛化标准贝叶斯说服问题中凹闭包定义的函数来刻画发送者期望效用的上确界。基于这一刻画，我们首先研究了一种特例：发送者能够利用可行实验达到无可行性约束的标准贝叶斯说服问题的最优期望效用——这是一个平凡效用上界——并在此情况下建立了关于发送者最优序贯设计的结构性结论。随后，我们推导了发送者最优序贯设计存在的条件；当最优序贯设计存在时，必存在一个马尔可夫性的最优设计，即下一实验的选择仅取决于接收者当前的信念。