Computing the Strong Nash Equilibrium For Conforming Coalitions

Abstract

Computing the equilibrium point of games plays an important in computer science. A large number of methods are known for finding a Nash equilibrium. Nevertheless, Nash equilibrium can be adopted only for non-cooperative games. In the last years, there has been a substantial effort in the development methods for finding the Strong Nash Equilibrium useful when coalitions are a fundamental issue. In this paper we present a new method for computing strong Nash equilibria in multiplayer games for a class of ergodic controllable Markov chains. For solving the problem we propose a two steps approach: a) we employ a regularized Lagrange principle to construct the Pareto front and b) we regularized the resulting Pareto front using the Tikhonov’s regularization method for ensuring the existence of a unique equilibrium and make use of the Newton method for converging to the Strong Nash equilibrium. A numerical example illustrates the efficiency of the approach.