Tie-breaking Agnostic Lower Bound for Fictitious Play
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913939788398592 |
|---|---|
| author | Wang, Yuanhao |
| author_facet | Wang, Yuanhao |
| contents | Fictitious play (FP) is a natural learning dynamic in two-player zero-sum games. Samuel Karlin conjectured in 1959 that FP converges at a rate of $O(t^{-1/2})$ to Nash equilibrium, where $t$ is the number of steps played. However, Daskalakis and Pan disproved the stronger form of this conjecture in 2014, where \emph{adversarial} tie-breaking is allowed.
This paper disproves Karlin's conjecture in its weaker form. In particular, there exists a 10-by-10 zero-sum matrix game, in which FP converges at a rate of $Ω(t^{-1/3})$, and no ties occur except for the first step. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tie-breaking Agnostic Lower Bound for Fictitious Play Wang, Yuanhao Computer Science and Game Theory Fictitious play (FP) is a natural learning dynamic in two-player zero-sum games. Samuel Karlin conjectured in 1959 that FP converges at a rate of $O(t^{-1/2})$ to Nash equilibrium, where $t$ is the number of steps played. However, Daskalakis and Pan disproved the stronger form of this conjecture in 2014, where \emph{adversarial} tie-breaking is allowed. This paper disproves Karlin's conjecture in its weaker form. In particular, there exists a 10-by-10 zero-sum matrix game, in which FP converges at a rate of $Ω(t^{-1/3})$, and no ties occur except for the first step. |
| title | Tie-breaking Agnostic Lower Bound for Fictitious Play |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2507.09902 |