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In this paper, a large class of time-varying Riccati equations arising instochastic dynamic games is considered. The problem of the existence anduniqueness of some globally defined solution, namely the bounded andstabilizing solution, is investigated. As an application of the obtainedexistence results, we address in a second step the problem of infinite-horizonzero-sum two players linear quadratic (LQ) dynamic game for a stochasticdiscrete-time dynamical system subject to both random switching of itscoefficients and multiplicative noise. We show that in the solution of such anoptimal control problem, a crucial role is played by the unique bounded andstabilizing solution of the considered class of generalized Riccati equations.

On the existence of the stabilizing solution of generalized Riccati equations arising in zero sum stochastic difference games: The time-varying case