Zero-Sum Games and Linear Programming Duality

Bernhard von Stengel

Mathematics of Operations Research, 2024, vol. 49, issue 2, 1091-1108

Abstract: The minimax theorem for zero-sum games is easily proved from the strong duality theorem of linear programming. For the converse direction, the standard proof by Dantzig is known to be incomplete. We explain and combine classical theorems about solving linear equations with nonnegative variables to give a correct alternative proof more directly than Adler. We also extend Dantzig’s game so that any max-min strategy gives either an optimal LP solution or shows that none exists.

Keywords: Primary: 91A05; secondary: 90C05; zero-sum game; minimax theorem; linear programming duality; lemma of Farkas (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:49:y:2024:i:2:p:1091-1108

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