Asymptotic Solutions to Weakly Coupled Stochastic Teams with Nonclassical Information

In this paper, we develop a new iterative approach toward the solution of a class of two-agent dynamic stochastic teams with nonclassical information when the coupling between the agents is weak, either through the state dynamics or through the information channel. In each case, the weak coupling is characterized in terms of a small (perturbation) parameter. When this parameter value (say, E ) is set equal to zero, the original fairly complex dynamic team, with a nonclassical information pattern, is decomposed into or converted to relatively simple stochastic control or team problems, the solution of which makes up the zeroth-order approximation (in a function space) to the team-optimal solution of the original problem. The fact that the zeroth-order solution approximates the optimal cost up to at least O ( E ) is shown by upper and lower bounding the optimal cost, and then proving that the zeroth-order terms of these bounds are identical. Using this zeroth-order term as the starting point for a policy iteration, we show that approximations of all orders can be obtained by solving a sequence of stochastic control and/or simpler team problems.