Factorization and escorting in the game-theoretical approach to non-extensive entropy measures

The game-theoretical approach to non-extensive entropy measures of statistical physics is based on an abstract measure of complexity from which the entropy measure is derived in a natural way. A wide class of possible complexity measures is considered and a property of factorization, apparently related to escorting, is investigated. It is shown that only those complexity measures which are connected with Tsallis entropy have the factorization property.