Computing the Stackelberg/Nash equilibria using the extraproximal method: Convergence analysis and implementation details for Markov chains games - Trejo, Kristal K.; Clempner, Julio B.; Poznyak, Alexander S. (Zielona Góra: Uniwersytet Zielonogórski)
In this paper we present the extraproximal method for computing the Stackelberg/Nash equilibria in a class of ergodic controlled finite Markov chains games. We exemplify the original game formulation in terms of coupled nonlinear programming problems implementing the Lagrange principle. In addition, Tikhonov`s regularization method is employed to ensure the convergence of the cost-functions to a Stackelberg/Nash equilibrium point. Then, we transform the problem into a system of equations in the proximal format.
Keywords: extraproximal method; Stackelberg games; convergence analysis; Markov chains; implementation