On a discrete-time linear jump stochastic dynamic game

In this paper we optimally solve a stochastic perfectly observed dynamic ga me for discrete-time linear systems with Markov jump parameters (LSMJPs). T he results here encompass both the cooperative and non-cooperative case. In cluded also, is a verification theorem. Besides being interesting in its ow n right, the motivation here lies, inter alia, in the results of recent vin tage, which show that, for the classical linear case, the risk-sensitive op timal control problem approach is intimately bound up with the H-infinity a nd game theoretical approach as given, for example, by Glover and Doyle. Th e 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 furt her inroads in the risk sensitivity problem for the LSJMPs.