Patience of matrix games

For matrix games we study how small nonzero probability must be used in optimal strategies. We show that for nxn 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 nxn win-lose game such that the unique optimal strategy uses a nonzero probability as small as n^-^@W^(^n^). This is done by constructing an explicit (-1,1) nonsingular nxn matrix, for which the inverse has only nonnegative entries and where some of the entries are of value n^@W^(^n^).

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