Abstract
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 detecting 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 afterward. 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 outperforms any other information disclosure strategy presented in the literature. We also show that our results can be extended to the infinite-horizon problem, to the problem where the matrix of transition probabilities of the Markov chain is time-varying, and to the case where the Markov chain has more than two states and one of the states is absorbing.
Highlights
The decentralization of information is an inevitable facet of managing a large system
The contribution of this paper is threefold. (i) The novelty of our model. (ii) The analytical approach to the solution of the dynamic information design problem. This approach is based on technical arguments that are different from the standard concavification method that is commonly used in the information design literature. (iii) The extension of our results to n-state Markov chains containing one absorbing state
We describe the optimal sequential information disclosure mechanism we propose for the solution to this problem in Sect
Summary
The decentralization of information is an inevitable facet of managing a large system. The game-form/mechanism is fixed but the system’s information structure is not fixed It has to be designed by the coordinator through the sequential disclosure/provision of information to the strategic agents so as to serve his goal (see [12,18,74] and references therein). Information design problems in dynamic environments involving a principal and longterm-optimizing strategic agents are challenging We focus on a very simple problem that allows us to highlight how sequential information provision/disclosure strategies can be designed in dynamic environments with long-term optimizing strategic agents. For each fixed sequential information disclosure policy of the principal, the detector is faced with a standard quickest detection problem with noisy observations. This approach is based on technical arguments that are different from the standard concavification method that is commonly used in the information design literature (see literature survey in Sect. 1.1). (iii) The extension of our results to n-state Markov chains containing one absorbing state
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