The game of normal numbers
成果类型：
Article
署名作者：
Lehrer, E
署名单位：
Tel Aviv University
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.1030.0087
发表日期：
2004
页码：
259-265
关键词：
摘要：
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(n(2)) calculations. The proof uses approachability in infinite-dimensional spaces (Lehrer 2002).
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