An algorithm for determining the decision thresholds in a distributed detection problem

A decentralized binary hypothesis-testing problem is considered in which a number of subordinate decision makers (DMs) transmit their opinions, based on their own data, to a primary decision maker who, in turn, combines the opinions with his own data to make the final team decision. The necessary conditions for the person-by-person optimal decision rules of the DMs are derived. A nonlinear Gauss-Seidel iterative algorithm is developed to solve for the decision thresholds of a person-by-person optimal strategy. The algorithm is illustrated with several examples, and implications for distributed organizational design are pointed out