Zero-Sum Games and Linear Programming Duality
成果类型：
Article; Early Access
署名作者：
von Stengel, Bernhard
署名单位：
University of London; London School Economics & Political Science
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2022.0149
发表日期：
2023
关键词：
摘要：
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.