We initiate the study of congestion games with variable demands where the
(variable) demand has to be assigned to exactly one subset of resources. The
players' incentives to use higher demands are stimulated by non-decreasing and
concave utility functions. The payoff for a player is defined as the difference
between the utility of the demand and the associated cost on the used
resources. Although this class of non-cooperative games captures many elements
of real-world applications, it has not been studied in this generality, to our
knowledge, in the past.