Dynamic Information Design: A Simple Problem on Optimal Sequential Information Disclosure

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