We study a dynamic information design problem in a finite-horizon setting consisting of two strategic and long-term optimizing agents, namely a principal (he) and a detector (she). The principal observes the evolution of a Markov chain that has two states, one "good" and one "bad" absorbing state, and has to decide how to sequentially disclose information to the detector. The detector's only information consists of the messages she receives from the principal. The detector's objective is to detect as accurately as possible the time of the jump from the good to the bad state. The principal's objective is to delay the detector as much as possible from detective the jump to the bad state. For this setting, we determine the optimal strategies of the principal and the detector. The detector's optimal strategy is described by time-varying thresholds on her posterior belief of the good state. We prove that it is optimal for the principal to give no information to the detector before a time threshold, run a mixed strategy to confuse the detector at the threshold time, and reveal the true state afterwards. We present an algorithm that determines both the optimal time threshold and the optimal mixed strategy that could be employed by the principal. We show, through numerical experiments, that this optimal sequential mechanism significantly outperforms any other information disclosure strategy presented in literature.

中文翻译：

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动态信息设计：一个关于最优顺序信息披露的简单问题

我们在有限范围设置中研究动态信息设计问题，该设置由两个战略和长期优化代理组成，即委托人 (he) 和检测器 (she)。校长观察具有两种状态的马尔可夫链的演化，一种“好”和一种“坏”吸收状态，并且必须决定如何顺序地向检测器公开信息。检测器的唯一信息包括她从委托人那里收到的消息。检测器的目标是尽可能准确地检测从良好状态跳到不良状态的时间。校长的目标是尽可能延迟检测器从检测器跳转到坏状态。对于此设置，我们确定主体和检测器的最佳策略。探测器' s 的最佳策略由她对良好状态的后验信念的时变阈值描述。我们证明了主体在时间阈值之前不向检测器提供任何信息，运行混合策略在阈值时间混淆检测器，然后揭示真实状态是最佳的。我们提出了一种算法，该算法可以确定委托人可以采用的最佳时间阈值和最佳混合策略。我们通过数值实验表明，这种最优顺序机制明显优于文献中提出的任何其他信息披露策略。运行混合策略在阈值时间混淆检测器，然后揭示真实状态。我们提出了一种算法，该算法可以确定委托人可以采用的最佳时间阈值和最佳混合策略。我们通过数值实验表明，这种最优顺序机制明显优于文献中提出的任何其他信息披露策略。运行混合策略在阈值时间混淆检测器，然后揭示真实状态。我们提出了一种算法，该算法可以确定委托人可以采用的最佳时间阈值和最佳混合策略。我们通过数值实验表明，这种最优顺序机制明显优于文献中提出的任何其他信息披露策略。