In many dynamic networks, control authorities seek for heterogeneous and even partially conflicting subobjectives. The misaligned interests threaten reliability of dynamic networks and degrade their operating performance. In this paper, we focus on design and analysis of mechanisms where a system operator provides a reward to incentivize control authorities to implement distributed stabilizing controllers. The proposed mechanisms are based on a bidding scheme where the bid of each control authority is represented by a newly derived local stability index. The mechanism induces a non-cooperative game between local control authorities while minimizing disclosures of their private information. By perturbing the game, we design an optimal incentive mechanism where the system operator can ensure network-wide stability and simultaneously maximize a social welfare while minimizing the reward size and perturbations.