Nash Bargaining Equilibria for Controllable Markov Chains Games

Abstract

A classical bargaining situation involves two individuals who have the opportunity to collaborate for mutual benefit. In this paper we present a novel approach for computing the Nash bargaining equilibrium for controllable Markov chains games. We follow the solution introduced by Nash considering the disagreement point as the Nash equilibrium of the problem. For solving the bargaining process we consider the game formulation in terms of nonlinear programming equations implementing the regularized Lagrange method. For computing the equilibrium point we employ the extraproximal optimization approach. We present the convergence and rate of convergence of the method. Finally a numerical example for a two-person bargaining situation illustrates the effectiveness of the method.