  A general model of decentralized stochastic control called partial history
sharing information structure is presented. In this model, at each step the
controllers share part of their observation and control history with each
other. This general model subsumes several existing models of information
sharing as special cases. Based on the information commonly known to all the
controllers, the decentralized problem is reformulated as an equivalent
centralized problem from the perspective of a coordinator. The coordinator
knows the common information and select prescriptions that map each
controller's local information to its control actions. The optimal control
problem at the coordinator is shown to be a partially observable Markov
decision process (POMDP) which is solved using techniques from Markov decision
theory. This approach provides (a) structural results for optimal strategies,
and (b) a dynamic program for obtaining optimal strategies for all controllers
in the original decentralized problem. Thus, this approach unifies the various
ad-hoc approaches taken in the literature. In addition, the structural results
on optimal control strategies obtained by the proposed approach cannot be
obtained by the existing generic approach (the person-by-person approach) for
obtaining structural results in decentralized problems; and the dynamic program
obtained by the proposed approach is simpler than that obtained by the existing
generic approach (the designer's approach) for obtaining dynamic programs in
decentralized problems.
