Mobile edge computing is one of the key enabling technologies of smart industry solutions, providing agile and ubiquitous services for mobile devices (MDs) through offloading latency-critical tasks to edge service providers. However, it is challenging to make optimal decisions of computation offloading and resource allocation while ensuring the privacy and information security of MDs. Consequently, we consider a new vision of digital twin (DT) empowered edge networks, where the optimization problem is formulated as a two-stage incentive mechanism. First, the resource allocation strategy is determined by the interaction among DTs according to the credit-based incentives. Afterward, a distributed incentive mechanism based on the Stackelberg-based alternating direction method of multipliers is opted to obtain the optimal offloading and privacy investment strategies in parallel. Numerical results show that the proposed two-stage incentive mechanism achieves effective resource allocation and computation offloading while simultaneously improving the privacy and information security of MDs.