Stochastic Teams with Nonclassical Information Revisited: When is an Affine Law Optimal?

In this paper we consider a parameterized family of two-stage stochastic control problems with nonclassical information patterns, which includes the famous 1968 counterexample of Witsenhausen. We show that the parameter region can be partitioned into two regions, in one of which the optimal solution is linear whereas in the other it is inherently nonlinear. In the latter, the best piecewise-constant solution does not always outperform the best linear solution, whereas a linear plus piecewise-constant policy leads to a uniformly better performance in that region. Extensive numerical computations complement the study.