We consider two solution concepts for discounted stochastic games: Stationary Strong Stackelberg Equilibrium (SSSE) and Fixed Point Equilibrium (FPE) solutions. The SSSE solution is obtained by explicitly solving the Stackelberg equilibrium conditions, while the FPE can be computed efficiently using value or policy iteration algorithms. We investigate the conditions for existence and equivalence of these solution concepts. We prove that the FPE and SSSE exist and coincide for important classes of games, including Myopic Follower Strategy and Team games. This however does not hold in general and we describe examples where one of SSSE or FPE does not exist, or when they both exist, they differ.
