Prosperity is associated with instability in dynamical networks

► Dynamic network model: newcomers copy strategies and links of successful role-models. ► Cooperators are prosperous, well-connected, but vulnerable to invasion by defectors. ► Defectors fragment networks which are re-formed by invasions of cooperators. ► Cooperation is favoured, but conflicts lead to perennial formation and fragmentation. ► Imitation leads to a trade-off between global welfare and stability.