Article ID Journal Published Year Pages File Type
419934 Discrete Applied Mathematics 2013 20 Pages PDF
Abstract

For matrix games we study how small nonzero probability must be used in optimal strategies. We show that for n×nn×n win–lose–draw games (i.e.  (−1,0,1)(−1,0,1) matrix games) nonzero probabilities smaller than n−O(n)n−O(n) are never needed. We also construct an explicit n×nn×n win–lose game such that the unique optimal strategy uses a nonzero probability as small as n−Ω(n)n−Ω(n). This is done by constructing an explicit (−1,1)(−1,1) nonsingular n×nn×n matrix, for which the inverse has only nonnegative entries and where some of the entries are of value nΩ(n)nΩ(n).

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Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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