An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games

This paper presents a novel approach for computing the strong Stackelberg/Nash equilib-rium for Markov chains games. For solving the cooperative n-leaders and m-followers Markov game we consider the minimization of the L_p-norm that reduces the distance to the utopian point in the Euclidian space. Then, we reduce the optimization problem to find a Pareto optimal solution. We employ a bi-level programming method implemented by the extraproximal optimization approach for computing the strong L_p-Stackelberg/Nash equilibrium. We validate the proposed method theoretically and by a numerical experiment related to marketing strategies for supermarkets.