Stability of linear stochastic difference equations in controlled random environments

We consider the stochastic sequence {Yi}t E N defined recursively by the linear relation Yt+l = AtYt + Bt in a random environment. The environment is described by the stochastic process {(At, Bt ) }t E N and is under the simultaneous control of several agents playing a discounted stochastic game. We formulate sufficient conditions on the game which ensure the existence of Nash equilibrium in Markov strategies which has the additional property that, in equilibrium, the process {Yt} t E N converges in distribution to a unique stationary sequence.