  This paper studies convex stochastic dynamic team problems with finite and
infinite time horizons under decentralized information structures. First, we
introduce two notions called exchangeable teams and symmetric information
structures. We show that in convex exchangeable team problems an optimal policy
exhibits a symmetry structure. We give a characterization for such
symmetrically optimal teams for a general class of convex dynamic team problems
under a mild conditional independence condition. In addition, through
concentration of measure arguments, we establish the convergence of optimal
policies for teams with $N$ decision makers to the corresponding optimal
policies for symmetric mean-field teams with infinitely many decision makers.
As a by-product, we present an existence result for convex mean-field teams,
where the main contribution of our paper is with respect to the information
structure in the system when compared with the related results in the
literature that have either assumed a classical information structure or a
static information structure. We also apply these results to the important
special case of Linear Quadratic Gaussian (LQG) team problems, where while for
partially nested LQG team problems with finite time horizons it is known that
the optimal policies are linear, for infinite horizon problems the linearity of
optimal policies has not been established in full generality. We also study
average cost finite and infinite horizon dynamic team problems with a symmetric
partially nested information structure and obtain globally optimal solutions
where we establish linearity of optimal policies.
