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We consider the ferromagnetic large-$q$ state Potts model in complex evolvingnetworks, which is equivalent to an optimal cooperation problem, in which theagents try to optimize the total sum of pair cooperation benefits and thesupports of independent projects. The agents are found to be typically of twokinds: a fraction of $m$ (being the magnetization of the Potts model) belongsto a large cooperating cluster, whereas the others are isolated one man'sprojects. It is shown rigorously that the homogeneous model has a stronglyfirst-order phase transition, which turns to second-order for randominteractions (benefits), the properties of which are studied numerically on theBarab\'asi-Albert network. The distribution of finite-size transition points ischaracterized by a shift exponent, $1/\tilde{\nu}'=.26(1)$, and by a differentwidth exponent, $1/\nu'=.18(1)$, whereas the magnetization at the transitionpoint scales with the size of the network, $N$, as: $m\sim N^{-x}$, with$x=.66(1)$.

Rounding of first-order phase transitions and optimal cooperation in scale-free networks