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Stationary Strong Stackelberg Equilibrium in Discounted Stochastic Games

Víctor Bucarey 1, 2 Eugenio Della Vecchia 3 Alain Jean-Marie 4 Fernando Ordóñez 5
2 INOCS - Integrated Optimization with Complex Structure
ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
4 NEO - Network Engineering and Operations
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this work we focus on Stackelberg equilibria for discounted stochastic games. 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, and we prove via counterexamples that SSSE does not exist in the general case. We define suitable dynamic programming operators whose fixed points are referred to as Fixed Point Equilibrium (FPE). We show that the FPE and SSSE coincide for a class of games with Myopic Follower Strategy. We provide numerical examples that shed light on the relationship between SSSE and FPE and the behavior of Value Iteration, Policy Iteration and Mathematical programming formulations for this problem. Finally, we present a security application to illustrate the solution concepts and the efficiency of the algorithms studied in this article.
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Submitted on : Monday, September 30, 2019 - 1:34:26 PM
Last modification on : Tuesday, November 19, 2019 - 5:30:45 PM


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  • HAL Id : hal-02144095, version 2


Víctor Bucarey, Eugenio Della Vecchia, Alain Jean-Marie, Fernando Ordóñez. Stationary Strong Stackelberg Equilibrium in Discounted Stochastic Games. [Research Report] RR-9271, INRIA. 2019, pp.62. ⟨hal-02144095v2⟩



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