COMMENTS ON J. VON NEUMANN'S 'THE PROBLEM OF OPTIMAL ASSIGNMENT IN A TWO-PERSON GAME'
Abstract
Certain arguments in J. von Neumann's 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 author's 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 21, 1952
- Accession Number
- AD0604238
Entities
People
- G. B. Dantzig
Organizations
- RAND Corporation