Decentralized optimal control of Markov chains with a common past information set

Decentralized dynamic (closed-loop) optimal control strategies are sought for a class of finite state Markov decision processes, characterized by the sharing of a common past after steps of delay. The control is considered over a finite time horizon, and it is shown that a nonclassical dynamic programming procedure can be applied, based on the existence of a sufficient statistic of constant dimension. Finally, the infinite horizon case is briefly discussed, in view of an extention of existing results on the minimization of average expected cost for the centralized and decentralized control of Markov chains.