On a discrete-time linear jump stochastic dynamic game

In this paper we optimally solve a stochastic perfectly observed dynamic game for discrete-time linear systems with Markov jump parameters (LSMJPs). The results here encompass both the cooperative and non-cooperative case. Included also, is a verification theorem. Besides being interesting in its own right, the motivation here lies, inter alia, in the results of recent vintage, which show that, for the classical linear case, the risk-sensitive optimal control problem approach is intimately bound up with the H-infinity and game theoretical approach as given, for example, by Glover and Doyle. The results derived here give a glimpse into how this connection may work in the linear jump case. This, in turn, gives some guidance and motivates further inroads in the risk sensitivity problem for the LSJMPs.