  We study distributed binary hypothesis testing with a single sensor and two
remote decision centers that are also equipped with local sensors. The
communication between the sensor and the two decision centers takes place over
three links: a shared link to both centers and an individual link to each of
the two centers. All communication links are subject to expected rate
constraints. This paper characterizes the optimal exponents region of the
type-II error for given type-I error thresholds at the two decision centers and
further simplifies the expressions in the special case of having only the
single shared link. The exponents region illustrates a gain under expected rate
constraints compared to equivalent maximum rate constraints. Moreover, it
exhibits a tradeoff between the exponents achieved at the two centers.
