A theory of sufficient statistics for teams

We introduce a theory of sufficient statistics for team decision problems. Starting from a rigorous definition of team sufficient statistics, we show that they contain all the information needed to make an optimal team decision. We also state general theorems of how to construct, manipulate, and update team sufficient statistics given the previous sufficient statistics and new measurements. Finally, we give the sufficient statistics for the class of partially nested team decision problems, and show that they have intuitive and compelling interpretations.