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 Lp-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 Lp-Stackelberg/Nash equilibrium. We validate the proposed method theoretically and by a numerical experiment related to marketing strategies for supermarkets.
Trejo, K. K., Clempner, J. B., & Poznyak, A. S. (2016). An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games. Kybernetika, 258-279. https://doi.org/10.14736/kyb-2016-2-0258