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The Kolmogorov complexity function K can be relativized using any oracle A,and most properties of K remain true for relativized versions. In section 1 weprovide an explanation for this observation by giving a game-theoreticinterpretation and showing that all "natural" properties are either true forall sufficiently powerful oracles or false for all sufficiently powerfuloracles. This result is a simple consequence of Martin's determinacy theorem,but its proof is instructive: it shows how one can prove statements aboutKolmogorov complexity by constructing a special game and a winning strategy inthis game. This technique is illustrated by several examples (total conditionalcomplexity, bijection complexity, randomness extraction, contrasting plain andprefix complexities).

Game interpretation of Kolmogorov complexity