  Motivated by the problem of utility allocation in a portfolio under a
Markowitz mean-variance choice paradigm, we propose an allocation criterion for
the variance of the sum of $n$ possibly dependent random variables. This
criterion, the Shapley value, requires to translate the problem into a
cooperative game. The Shapley value has nice properties, but, in general, is
computationally demanding. The main result of this paper shows that in our
particular case the Shapley value has a very simple form that can be easily
computed. The same criterion is used also to allocate the standard deviation of
the sum of $n$ random variables and a conjecture about the relation of the
values in the two games is formulated.
