  In this paper we study the cooperative behavior of agents playing the
Prisoner's Dilemma game in random scale-free networks. We show that the
survival of cooperation is enhanced with respect to random homogeneous graphs
but, on the other hand, decreases when compared to that found in
Barab\'asi-Albert scale-free networks. We show that the latter decrease is
related with the structure of cooperation. Additionally, we present a mean
field approximation for studying evolutionary dynamics in networks with no
degree-degree correlations and with arbitrary degree distribution. The mean
field approach is similar to the one used for describing the disease spreading
in complex networks, making a further compartmentalization of the strategists
partition into degree-classes. We show that this kind of approximation is
suitable to describe the behavior of the system for a particular set of initial
conditions, such as the placement of cooperators in the higher-degree classes,
while it fails to reproduce the level of cooperation observed in the numerical
simulations for arbitrary initial configurations.
