The team ROC curve in a binary hypothesis testing environment

We consider the distributed detection problem, in which a set of decision makers (DMs) receive observations of the environment and transmit finite-valued messages to other DMs according to prespecified communication protocols. A designated primary DM makes the find decision on one out of two alternative hypotheses. All DMs make decisions, in order to maximize a measure of organizational performance. We discuss three different types of decision rules (deterministic, independent randomization, and dependent randomization), and their implications on the organizational performance. Each DM is described by its individual receiver operating characteristic (ROC) curve, which is concave. We determine that concavity is not guaranteed for the case of the ROC curve of a team of DMs, even if the decision rules are perfectly continuous and if the individual ROC curves are strictly concave and smooth unless dependent randomization is allowed