Approximation schemes for stochastic teams with weakly coupled agents

The main objective of this paper is to develop a new iterative approach towards the solution of dynamic stochastic teams when the coupling among a subset of agents is weak, either through the state dynamics or through the performance index. In each case, the weak coupling is characterized in terms of a number of small (perturbation) parameters. When these parameter values are set equal to zero, the original fairly complex dynamic team, with a quasiclassical or a nonclassical information pattern is decomposed into relatively simpler stochastic control and team problems, the solution of which make up the zeroth order approximation (in a function space) to the team-optimal solution of the original problem. Using this as a starting point for an iteration, we show that approximations of all orders can be obtained by solving a sequence of stochastic control and/or simpler team problems. The paper studies, particularly, two agent LQG teams with quasiclassical or nonclassical information patterns, but the approach is applicable to other models (with more than two agents and non-Gaussian statistics) as well.