  This paper studies the monotonicity of equilibrium costs and equilibrium
loads in nonatomic congestion games, in response to variations of the demands.
The main goal is to identify conditions under which a paradoxical non-monotone
behavior can be excluded. In contrast to routing games with a single commodity,
where the network topology is the sole determinant factor for monotonicity, for
general congestion games with multiple commodities the structure of the
strategy sets plays a crucial role.
  We frame our study in the general setting of congestion games, with a special
focus on singleton congestion games, for which we establish the monotonicity of
equilibrium loads with respect to every demand. We then provide conditions for
comonotonicity of the equilibrium loads, i.e., we investigate when they jointly
increase or decrease after variations of the demands. We finally extend our
study from singleton congestion games to the larger class of constrained
series-parallel congestion games, whose structure is reminiscent of the concept
of a series-parallel network.
