Zero-Sum Games and Linear Programming Duality

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 (1951) 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 (2013). We also extend Dantzig's game so that any max-min strategy gives either an optimal LP solution or shows that none exists.

v6: Corrected year in date, shorter proof of Farkas using Thm 10 (minimal infeasibility, page 27, shows y>0). Equations read better than in MOR version

Cited by in corpus (1)

• On the Equivalence of Zero-Sum Games and Conic Programs