Zero-sum games and linear programming duality

Von Stengel, Bernhard ORCID: 0000-0002-3488-8322 (2023) Zero-sum games and linear programming duality. Mathematics of Operations Research. ISSN 0364-765X

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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.

Item Type:	Article
Additional Information:	© 2023 INFORMS
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	17 Nov 2023 12:18
Last Modified:	18 Dec 2023 09:45
URI:	http://eprints.lse.ac.uk/id/eprint/120779

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