  This paper considers two problems -- a dynamic team problem and a
decentralized control problem. The problems we consider do not belong to the
known classes of "simpler" dynamic team/decentralized control problems such as
partially nested or quadratically invariant problems. However, we show that our
problems admit simple solutions under an assumption referred to as the
substitutability assumption. Intuitively, substitutability in a team (resp.
decentralized control) problem means that the effects of one team member's
(resp. controller's) action on the cost function and the information (resp.
state dynamics) can be achieved by an action of another member (resp.
controller). For the non-partially-nested LQG dynamic team problem, it is shown
that under certain conditions linear strategies are optimal. For the
non-partially-nested decentralized LQG control problem, the state structure can
be exploited to obtain optimal control strategies with recursively update-able
sufficient statistics. These results suggest that substitutability can work as
a counterpart of the information structure requirements that enable
simplification of dynamic teams and decentralized control problems.
