Computing all Nash equilibria of low-rank bi-matrix games
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912587550031872 |
|---|---|
| author | Feinstein, Zachary Löhne, Andreas Rudloff, Birgit |
| author_facet | Feinstein, Zachary Löhne, Andreas Rudloff, Birgit |
| contents | We study constrained bi-matrix games, with a particular focus on low-rank games. Our main contribution is a framework that reduces low-rank games to smaller, equivalent constrained games, along with a necessary and sufficient condition for when such reductions exist. Building on this framework, we present three approaches for computing the set of extremal Nash equilibria, based on vertex enumeration, polyhedral calculus, and vector linear programming. Numerical case studies demonstrate the effectiveness of the proposed reduction and solution methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11718 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computing all Nash equilibria of low-rank bi-matrix games Feinstein, Zachary Löhne, Andreas Rudloff, Birgit Optimization and Control We study constrained bi-matrix games, with a particular focus on low-rank games. Our main contribution is a framework that reduces low-rank games to smaller, equivalent constrained games, along with a necessary and sufficient condition for when such reductions exist. Building on this framework, we present three approaches for computing the set of extremal Nash equilibria, based on vertex enumeration, polyhedral calculus, and vector linear programming. Numerical case studies demonstrate the effectiveness of the proposed reduction and solution methods. |
| title | Computing all Nash equilibria of low-rank bi-matrix games |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2509.11718 |