Zero-Sum Games and Linear Programming Duality

05/23/2022

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by   Bernhard von Stengel, et al.

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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 (1951) is massively incomplete, as we argue in this article. We explain and combine classical theorems about solving linear equations with nonnegative variables to give a correct alternative proof.