Résumé : In this work we study strong Stackelberg equilibria in stationary policies for discounted stochastic games, named (SSSE). We provide classes of games where the SSSE exists, and we prove via counterxamples that SSSE does not exist in the general case. We define suitable dynamic programming operators and we study their fixed points, named FPE. We show that the FPE and SSSE coincides for some games. In particular, we introduce the class of games with Myopic Follower Strategy, which have this property. We study the behaviour of Value Iteration, Policy Iteration and Mathematical programming formulations for this problem. Finally, we show an application in security in order to test the solution concepts and the efficiency of the algorithms studied in this article.