Threshold repetition for entangled games. Proves exponential threshold repetition for every finite two-player one-round game: if its entangled value is v < 1, the probability of winning at least a fraction $v+\delta$ of k independent repetitions decays exponentially in k, for $0\lt \delta\lt 1-v$. Arbitrary joint finite-dimensional entangled strategies and correlated question distributions are allowed.
released 2026-09-25 | 1 theorem · 6 lemmas · 11 proofs · 7,151 words |
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For every finite two-player game with entangled value v < 1, we prove exponential decay for the probability of winning at least a $v+\delta$ fraction of k independent repetitions, uniformly over all finite-dimensional joint strategies. The result allows arbitrary correlated question distributions and holds for every $0\lt \delta\lt 1-v$ and k ≥ 1. Its universal rate is proportional to $\delta^5/(1+\log(|\mathcal A||\mathcal B|))$, where $\mathcal A,\mathcal B$ are the answer alphabets. For each fixed question distribution, we also obtain an explicit cubic rate in δ.