We consider a two-player dynamic information design problem between a principal and a receiver -- a game is played between the two agents on top of a Markovian system controlled by the receiver's actions, where the principal obtains and strategically shares some information about the underlying system with the receiver in order to influence their actions. In our setting, both players have long-term objectives, and the principal sequentially commits to their strategies instead of committing at the beginning. Further, the principal cannot directly observe the system state, but at every turn they can choose randomized experiments to observe the system partially. The principal can share details about the experiments to the receiver. For our analysis we impose the truthful disclosure rule: the principal is required to truthfully announce the details and the result of each experiment to the receiver immediately after the experiment result is revealed. Based on the received information, the receiver takes an action when its their turn, with the action influencing the state of the underlying system. We show that there exist Perfect Bayesian equilibria in this game where both agents play Canonical Belief Based (CBB) strategies using a compressed version of their information, rather than full information, to choose experiments (for the principal) or actions (for the receiver). We also provide a backward inductive procedure to solve for an equilibrium in CBB strategies.

翻译：我们考虑主理人与接收者之间的双人动态信息设计问题——两个智能体在由接收者行动控制的马尔可夫系统之上进行博弈，主理人获取关于底层系统的某些信息并有策略地分享给接收者，以影响后者的行动。在我们的设定中，双方都具有长期目标，且主理人并非在博弈开始时一次性承诺其策略，而是逐轮进行序列化承诺。此外，主理人无法直接观测系统状态，但每轮可通过选择随机实验来部分观测系统。主理人可向接收者透露实验细节。为便于分析，我们施加“真实披露规则”：主理人被要求在每轮实验结果揭晓后立即向接收者如实公布实验细节与结果。接收者基于所获信息在其轮次中采取行动，而该行动会影响底层系统的状态。我们证明，在该博弈中存在完美贝叶斯均衡，其中双方采用“基于典型信念”（CBB）策略，即使用压缩后的信息版本（而非全部信息）来选择实验（对主理人而言）或行动（对接收者而言）。我们还提供了一种逆向归纳程序，用于求解CBB策略下的均衡。