Patience of Matrix Games - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Discrete Applied Mathematics Year : 2013

Patience of Matrix Games


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 $n^{\Omega(n)}$.
Fichier principal
Vignette du fichier
MatrixGamePatience_revision.pdf (428.58 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-00843052 , version 1 (10-07-2013)



Kristoffer Arnsfelt Hansen, Rasmus Ibsen-Jensen, Vladimir V. Podolskii, Elias Tsigaridas. Patience of Matrix Games. Discrete Applied Mathematics, 2013, ⟨10.1016/j.dam.2013.05.008⟩. ⟨hal-00843052⟩
208 View
165 Download



Gmail Mastodon Facebook X LinkedIn More