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            <funder>Victor Bucarey has been partially supported by the Fonds de la Recherche Scientifique-FNRS under Grant(s) n° PDR T0098.18.</funder>
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                <term xml:lang="en">Stackelberg Equilibrium</term>
                <term xml:lang="en">Optimal control</term>
                <term xml:lang="en">Stochastic games</term>
                <term xml:lang="fr">Équilibre de Stackelberg</term>
                <term xml:lang="fr">Contrôle optimal</term>
                <term xml:lang="fr">Jeux stochastiques</term>
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              <p>In this work we focus on Stackelberg equilibria for discounted stochasticgames. We begin by formalizing the concept of Stationary Strong Stackelberg Equlibrium(SSSE) policies for such games. We provide classes of games where the SSSE exists, andwe prove via counterexamples that SSSE does not exist in the general case. We definesuitable dynamic programming operators whose fixed points are referred to as FixedPoint Equilibrium (FPE). We show that the FPE and SSSE coincide for a class of gameswith Myopic Follower Strategy. We provide numerical examples that shed light on therelationship between SSSE and FPE and the behavior of Value Iteration, Policy Iterationand Mathematical programming formulations for this problem. Finally, we present asecurity application to illustrate the solution concepts and the efficiency of the algorithmsstudied in this article.</p>
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              <p>Dans cet article, nous nous focalisons sur les équilibres de Stackelbergpour pour les jeux stochastiques actualisés. Nous commençons par formaliser le conceptd’équilibre fort de Stackelberg en politiques stationnaires (Strong Stationary StackelbergEquilibria, SSSE) pour ces jeux. Nous exhibons des classes de jeux pour lesquels le SSSEexiste et nous montrons par des contre-exemples que les SSSE n’existent pas dans le casgénéral. Nous définissons des opérateurs de programmation dynamique appropriés pour ceconcept dont les points fixes sont nommés FPE (Fixed Point Equilibria). Nous montronsque le FPE et le SSSE coïncident pour la classe de jeux stochastiques avec stratégiedu “follower” myope (Myopic Follower Strategy, MFS). Nous montrons des exemplesnumériques qui éclairent la relation entre SSSE et FPE ainsi que le comportement desalgorithmes Value Iteration, Policy Iteration, et la formulation par ProgrammationMathématique de ce problème. Finalement, nous décrivons une application dans ledomaine de la sécurité pour illustrer les concepts de solution et l’efficacité des algorithmesintroduits dans cet article.</p>
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