Patience of matrix games

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  • Kristoffer Arnsfelt Hansen
  • Rasmus Ibsen-Jensen, Denmark
  • Vladimir V. Podolskii, Steklov Mathematical Institute, Russian Federation
  • Elias Tsigaridas, Denmark
For matrix games we study how small nonzero probability must be used in optimal strategies. We show that for image win–lose–draw games (i.e. image matrix games) nonzero probabilities smaller than image are never needed. We also construct an explicit image win–lose game such that the unique optimal strategy uses a nonzero probability as small as image. This is done by constructing an explicit image nonsingular image matrix, for which the inverse has only nonnegative entries and where some of the entries are of value image.
Original languageEnglish
JournalDiscrete Applied Mathematics
Volume161
Issue16-17
Pages (from-to)2440–2459
Number of pages20
ISSN0166-218X
Publication statusPublished - 2013

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