AbstractOne of the diagrammatic methods for solving two‐person 2 ×nmatrix games can be extended to solvem×ngames where each column of the matrix is a concave function of the row number. This gives a simple proof of a theorem of Benjamin and Goldman that such games have solutions involving no more than two consecutive strategies for the row player, and no more than two strategies for the column player. Two extensions are discussed. © 1994 John Wiley&Sons,