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Lowness Properties of Reals and HyperImmunity
 In Wollic 2003
, 2003
"... AmbosSpies and Kucera [1, Problem 4.5] asked if there is a noncomputable set A which is low for the computably random reals. We show that no such A is of hyperimmune degree. Thus, each g T A is dominated by a computable function. AmbosSpies and Kucera [1, Problem 4.8] also asked if every Slo ..."
Abstract

Cited by 9 (2 self)
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AmbosSpies and Kucera [1, Problem 4.5] asked if there is a noncomputable set A which is low for the computably random reals. We show that no such A is of hyperimmune degree. Thus, each g T A is dominated by a computable function. AmbosSpies and Kucera [1, Problem 4.8] also asked if every Slow set is S 0 low. We give a partial solution to this problem, showing that no Slow set is of hyperimmune degree.
Complexity and Mixed Strategy Equilibria ∗
"... Unpredictable behavior is central for optimal play in many strategic situations because a predictable pattern leaves a player vulnerable to exploitation. A theory of unpredictable behavior is presented in the context of repeated twoperson zerosum games in which the stage games have no pure strateg ..."
Abstract
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Unpredictable behavior is central for optimal play in many strategic situations because a predictable pattern leaves a player vulnerable to exploitation. A theory of unpredictable behavior is presented in the context of repeated twoperson zerosum games in which the stage games have no pure strategy equilibrium. Computational complexity considerations are introduced to restrict players ’ strategy sets. The use of Kolmogorov complexity allows us to obtain a sufficient condition for equilibrium existence. The resulting theory has implications for the empirical literature that tests the equilibrium hypothesis in a similar context. In particular, the failure of some tests for randomness does not justify rejection of equilibrium play.