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- Title
Zero-Sum Games and Linear Programming Duality.
- Authors
von Stengel, Bernhard
- 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.
- Subjects
ZERO sum games; LINEAR programming; LINEAR equations
- Publication
Mathematics of Operations Research, 2024, Vol 49, Issue 2, p1091
- ISSN
0364-765X
- Publication type
Article
- DOI
10.1287/moor.2022.0149