In 1951, Dantzig showed the equivalence of linear programming and two-person zero-sum games. However, in the description of his reduction from linear programming to zero-sum games, he noted that there was one case in which his reduction does not work. This also led to incomplete proofs of the relationship between the Minmax Theorem of game theory and the Strong Duality Theorem of linear programming. In this note, we fill these gaps.
Manuscript, Depatrment of IEOR, University of California, Berkeley, CA 94720, June/2010