Stationary Strong Stackelberg Equilibrium in Discounted Stochastic Games

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.