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.