  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 investigated.
The property reflects a separation between the system being observed and the
observer. Apparently, the property is also related to escorting. It is shown
that only those complexity measures which are connected with Tsallis entropy
have the factorization property.
