Decentralized Detection with Signaling

We consider a sequential problem in decentralized detection. Two observers can make repeated noisy observations of a binary hypothesis on the state of the environment. At any time, any of the two observers can stop and send a final message to the other observer or it may continue to take more measurements. After an observer has sent its final message, it stops operating. The other observer is then faced with a different stopping problem. At each time instant, it can decide either to stop and declare a final decision on the hypothesis or take another measurement. At each time, the system incurs an operating cost depending on the number of observers that are active at that time. A terminal cost that measures the accuracy of the final decision is incurred at the end. We show that, unlike in other sequential detection problems, stopping rules characterized by two thresholds on an observer's posterior belief no longer guarantee optimality in this problem. Thus the potential for signaling among observers alters the nature of optimal policies. We obtain a new parametric characterization of optimal policies for this problem.