Patience of matrix games

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• 作者：Kristoffer Arnsfelt Hansen ; Rasmus Ibsen-Jensen ; Vladimir V. Podolskii ; Elias Tsigaridas
• 关键词：Matrix games ; Ill-conditioned matrices ; Nonnegative inverse
• 刊名：Discrete Applied Mathematics
• 出版年：2013
• 出版时间：November, 2013
• 年：2013
• 卷：161
• 期：16-17
• 页码：2440-2459
• 全文大小：484 K

文摘

For matrix games we study how small nonzero probability must be used in optimal strategies. We show that for win-lose-draw games (i.e.? matrix games) nonzero probabilities smaller than are never needed. We also construct an explicit win-lose game such that the unique optimal strategy uses a nonzero probability as small as . This is done by constructing an explicit nonsingular matrix, for which the inverse has only nonnegative entries and where some of the entries are of value .