Centralized Versus Decentralized Optimization of Distributed Stochastic Differential Decision Systems With Different Information Structures—Part II: Applications

Abstract

In this second part of the two-part paper, a stochastic maximum principle, conditional Hamiltonians, and the coupled backward-forward stochastic differential equations of the first part [1] are employed to derive decentralized team optimal strategies for distributed decision systems with different information structures. Examples of such team problems are presented in nonlinear and linear quadratic forms. In many cases, the expressions of the optimal decentralized strategies are obtained. An interesting feature of any one optimal decentralized strategy is the dependence on the conditional estimates of the other optimal responses. For team problems of linear quadratic form and independent nonanticipative information structures, any optimal strategy depends linearly on the mean values of the other optimal responses. This property makes their computation feasible, even for large-scale distributed systems with many decision makers (DMs). It is also related to mean field stochastic optimal control problems, with finite number of DMs. The examples presented illustrate the effect of information signaling among the DMs in reducing the computational complexity of optimal decentralized strategies.