Zero-Sum Games and Linear Programming Duality br

• 成果类型: Article
• 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
• 发表日期: 2024
• 页码: 1091-1108
• 关键词: NASH SOCIAL-WELFARE; budgeted allocations; Market equilibrium; satiation; algorithm; approximability; auctions; hardness; utility; prices

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 solv-ing 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