Weak sufficient statistics for team decision problems

The team sufficient statistics defined by Wu and Lall are known to be sufficient for optimality in team decision problems. In this paper we give a new mathematical characterization of these statistics, as well as a new intuitive interpretation in terms of the ability to simulate measurements. Then, we define a new class of statistics, which we call weak team sufficient statistics, and show that these statistics are not only sufficient for optimality, but also necessary for simultaneous optimality with respect to all cost functions.