Implications of contrarian and one-sided strategies for the fair-coin game

Details Implications of contrarian and one-sided strategies for the fair-coin game Implications of contrarian and one-sided strategies for the fair-coin game

2007-03-26

arxiv.org/abs/math/0703743v1

Stochastic Processes and their Applications 118 (2008) 2125-2142

Mathematics

Probability

Scientific paper

10.1016/j.spa.2007.11.007

We derive some results on contrarian and one-sided strategies by Skeptic for the fair-coin game in the framework of the game-theoretic probability of Shafer and Vovk \cite{sv}. In particular, concerning the rate of convergence of the strong law of large numbers (SLLN), we prove that Skeptic can force that the convergence has to be slower than or equal to $O(n^{-1/2})$. This is achieved by a very simple contrarian strategy of Skeptic. This type of result, bounding the rate of convergence from below, contrasts with more standard results of bounding the rate of SLLN from above by using momentum strategies. We also derive a corresponding one-sided result.

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