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 data to a primary decisionmaker who, in turn, combines the opinions with his own data to make the final team decision. The necessary conditions for the optimal decision rules of the DMs are derived. A nonlinear Gauss-Seidel iterative algorithm is developed for solving the decision thresholds of a person-by-person optimal strategy, and its monotonic convergence is established. The algorithm is illustrated with several examples, and implications for distributed organizational design are pointed out