IEOR - Designing a More Efficient World

The equivalence of linear programs and zero-sum games

Publication Date: April 2, 2012

Ilan Adler (2012), The equivalence of linear programs and zero-sum games, International Journal of Game Theory.


Abstract: In 1951, Dantzig showed the equivalence of linear programming problems and two-person zero-sum games. However, in the description of his reduction from linear programs to zero-sum games, he noted that there was one case in which the reduction does not work. This also led to incomplete proofs of the relationship between the Minimax Theorem of game theory and the Strong Duality Theorem of linear programming. In this note, we fill these gaps.