Extended matrix norm method: Applications to bimatrix games and convergence results

•Extension of the Matrix Norm (MN) approach and its applications to the nonzero-sum bimatrix games are presented.•Convergence results of the MN approaches are given.•An improved interval for the game value for the zero/nonzero sum matrix games is provided.•The consistency of the approaches is shown by various bimatrix game examples from the literature.•It is shown that a better estimate of the game value can be obtained by repeated applications of the extended matrix norm (EMN) method.