International Journal of Game Theory

, Volume 42, Issue 1, pp 165–177 | Cite as

The equivalence of linear programs and zero-sum games

  • Ilan Adler


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.


Linear programming Zero-sum games Minimax theorem Strong duality Farkas’ lemma Villes’ theorem 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of IEORUniversity of CaliforniaBerkeleyUSA

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