  We consider the ferromagnetic large-$q$ state Potts model in complex evolving
networks, which is equivalent to an optimal cooperation problem, in which the
agents try to optimize the total sum of pair cooperation benefits and the
supports of independent projects. The agents are found to be typically of two
kinds: a fraction of $m$ (being the magnetization of the Potts model) belongs
to a large cooperating cluster, whereas the others are isolated one man's
projects. It is shown rigorously that the homogeneous model has a strongly
first-order phase transition, which turns to second-order for random
interactions (benefits), the properties of which are studied numerically on the
Barab\'asi-Albert network. The distribution of finite-size transition points is
characterized by a shift exponent, $1/\tilde{\nu}'=.26(1)$, and by a different
width exponent, $1/\nu'=.18(1)$, whereas the magnetization at the transition
point scales with the size of the network, $N$, as: $m\sim N^{-x}$, with
$x=.66(1)$.
