Computing the Nash Bargaining Solution for Multiple Players in Discrete-Time Markov Chains Games

This paper presents a novel method for computing the Nash bargaining equilibrium for finite, ergodic and controllable Markov chains games. To solve the bargaining process we first set the disagreement point as the Nash equilibrium of the problem, then to find the new agreement point we follow the bargaining model presented by Nash. We exemplify the game formulation in terms of nonlinear programing equations implementing the Lagrange principle. For ensuring the convergence of the game to an equilibrium point we employ the Tikhonov's regularization method. For solving the bargaining problem we make use of the extraproximal optimization approach. Finally, we validate the proposed method by a numerical example for a three-person bargaining situation.