  This paper is concerned with the properties of the sets of strategic measures
induced by admissible team policies in decentralized stochastic control and the
convexity properties in dynamic team problems. To facilitate a convex
analytical approach, strategic measures for team problems are introduced.
Properties such as convexity, and compactness and Borel measurability under
weak convergence topology are studied, and sufficient conditions for each of
these properties are presented. These lead to existence of and structural
results for optimal policies. It will be shown that the set of strategic
measures for teams which are not classical is in general non-convex, but the
extreme points of a relaxed set consist of deterministic team policies, which
lead to their optimality for a given team problem under an expected cost
criterion. Externally provided independent common randomness for static teams
or private randomness for dynamic teams do not improve the team performance.
The problem of when a sequential team problem is convex is studied and
necessary and sufficient conditions for problems which include teams with a
non-classical information structure are presented. Implications of this
analysis in identifying probability and information structure dependent
convexity properties are presented.
