Convergence conditions for the Brown-Robinson iterative method for bimatrix games (Q1841137)

The author considers the Brown-Robinson iterative scheme for computing a mixed strategy equilibrium for a bimatrix game. It is known that such a scheme converges in the case of a zero-sum game. There are also examples to show that this convergence result does not hold if the game is a bimnatrix game. In this paper the author derives certain conditions on a bimatrix game for which the iterative scheme converges. A condition is that the given bimatrix game should be reducible to a zero-sum game by a composition of various transformations such as addition of a constant to any column of the first player's pay-off matrix, addition of a constant to any row in the second player's pay-off matrix, and multiplication of the pay-off matrix by a positive constant \(\alpha.\)