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Patience of Matrix Games

Abstract : For matrix games we study how small nonzero probability must be used in optimal strategies. We show that for $n \times n$ win-lose-draw games (i.e.\ $(-1,0,1)$ matrix games) nonzero probabilities smaller than $n^{-O(n)}$ are never needed. We also construct an explicit $n \times n$ win-lose game such that the unique optimal strategy uses a nonzero probability as small as $n^{-\Omega(n)}$. This is done by constructing an explicit $(-1,1)$ nonsingular $n \times n$ matrix, for which the inverse has only nonnegative entries and where some of the entries are of value $n^{\Omega(n)}$.
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Submitted on : Wednesday, July 10, 2013 - 11:59:39 AM
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Kristoffer Arnsfelt Hansen, Rasmus Ibsen-Jensen, Vladimir V. Podolskii, Elias Tsigaridas. Patience of Matrix Games. Discrete Applied Mathematics, Elsevier, 2013, ⟨10.1016/j.dam.2013.05.008⟩. ⟨hal-00843052⟩

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