Convex Symmetric Stochastic Dynamic Teams and Their Mean-Field Limit

This paper studies convex stochastic dynamic team problems with finite and infinite time horizons under decentralized information structures. First, we introduce the notions of 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. In addition, for convex mean-field teams with a symmetric information structure, through concentration of measure arguments, we establish the convergence of optimal policies for mean-field teams with N decision makers to the corresponding optimal policies of mean-field teams with countably infinite number of decision makers. As a by-product, we also present an existence result for convex mean-field teams. While for partially nested LQG team problems with finite time horizon 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 and typically not only linearity but also time-invariance and stability properties are imposed apriori in the literature. In this paper, 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. Moreover, we discuss average cost infinite horizon problems for LQG dynamic teams with sparsity and delay constraints.