The game of normal numbers

The game of normal numbers

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Article ID: iaor20072012
Country: United States
Volume: 29
Issue: 2
Start Page Number: 259
End Page Number: 265
Publication Date: May 2004
Journal: Mathematics of Operations Research
Authors:
Abstract:

We introduce a two-player game where at each period one player, say, Player 2, chooses a distribution and the other player, Player 1, chooses a realization. Player 1 wins the game if the sequence of realized outcomes is normal with respect to the sequence of distributions. We present a pure winning strategy of Player 1 and thereby provide a universal algorithm that generates a normal sequence for any discrete stochastic process. It turns out that to select the nth digit, the algorithm conducts O(n2) calculations. The proof uses approachability in infinite-dimensional spaces.

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