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This paper presents a novel approach for computing the strong Stackelberg/Nash equilibrium 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.

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