Patience of Matrix Games
Résumé
For matrix games we study how small nonzero probability must be used in optimal strategies. We show that for n×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×n win-lose game such that the unique optimal strategy uses a nonzero probability as small as n−Ω(n). This is done by constructing an explicit (−1,1) nonsingular n×n matrix, for which the inverse has only nonnegative entries and where some of the entries are of value nΩ(n).
Origine | Fichiers produits par l'(les) auteur(s) |
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