  We consider a decentralized system with multiple controllers and define
substitutability of one controller by another in open-loop strategies. We
explore the implications of this property on the optimization of closed-loop
strategies. In particular, we focus on the decentralized LQG problem with
substitutable actions. Even though the problem we formulate does not belong to
the known classes of "simpler" decentralized problems such as partially nested
or quadratically invariant problems, our results show that, under the
substitutability assumption, linear strategies are optimal and we provide a
complete state space characterization of optimal strategies. We also identify a
family of information structures that all give the same optimal cost as the
centralized information structure under the substitutability assumption. Our
results suggest that open-loop substitutability can work as a counterpart of
the information structure requirements that enable simplification of
decentralized control problems.
