COMMENTS ON J. VON NEUMANN'S 'THE PROBLEM OF OPTIMAL ASSIGNMENT IN A TWO-PERSON GAME'

Certain arguments in J. von Neumanns paper reducing the optimal assignment problem to a two-person game can be simplified. A simple observation produces a proof that all vertices of the convex of solutions or a related continuous problem are permutations hence, admissible solutions to the original combinatorial problem. This is a modification of the authors proof that optimal solution to the transportation problem is integral if the row and column totals are integers. The present proof depends on a well-known and easily verified theorem that the vertex of a convex defined by m-linear equations in n-non-negative variables considered as a point in R sub N has at most m positive components.