{"ID":2894654,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.09902","arxiv_id":"2507.09902","title":"Tie-breaking Agnostic Lower Bound for Fictitious Play","abstract":"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.","short_abstract":"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{ad...","url_abs":"https://arxiv.org/abs/2507.09902","url_pdf":"https://arxiv.org/pdf/2507.09902v1","authors":"[\"Yuanhao Wang\"]","published":"2025-07-14T04:15:17Z","proceeding":"cs.GT","tasks":"[\"cs.GT\"]","methods":"[]","has_code":false}