  In this paper, a large class of time-varying Riccati equations arising in
stochastic dynamic games is considered. The problem of the existence and
uniqueness of some globally defined solution, namely the bounded and
stabilizing solution, is investigated. As an application of the obtained
existence results, we address in a second step the problem of infinite-horizon
zero-sum two players linear quadratic (LQ) dynamic game for a stochastic
discrete-time dynamical system subject to both random switching of its
coefficients and multiplicative noise. We show that in the solution of such an
optimal control problem, a crucial role is played by the unique bounded and
stabilizing solution of the considered class of generalized Riccati equations.
