Zero-Sum Games and Linear Programming Duality
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915090795593728 |
|---|---|
| author | von Stengel, Bernhard |
| author_facet | von Stengel, Bernhard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_11196 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Zero-Sum Games and Linear Programming Duality von Stengel, Bernhard Computer Science and Game Theory Optimization and Control 91A05, 90C05 G.2 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. |
| title | Zero-Sum Games and Linear Programming Duality |
| topic | Computer Science and Game Theory Optimization and Control 91A05, 90C05 G.2 |
| url | https://arxiv.org/abs/2205.11196 |