Computing Nash Equilibria by Iterated Polymatrix Approximation

This article develops a new algorithm for computing a Nash equilibrium of an N-person game. The algorithm approximates the game by a sequence of polymatrix games. We provide su±cient conditions for local convergence to an equilibrium and report on our computational experience. The algorithm convergences rapidly but it is not failsafe. We show that if the algorithm does not converge then one can at any point switch easily to the Global Newton Method, which is slower but failsafe. Thus, the algorithm can be used to obtain a fast start for the Global Newton Method.