The recent expansion of mobile IoT devices (MIoTDs) along with the exposure of many compute-intensive and latency-critical applications, have given a step rise to the mobile edge computing (MEC) platform to process computational microservices at the edge. The paramount importance of designing an effective incentive mechanism is a very important topic for such systems to get a fair amount of resources and provide incentives to MIoDs. Hence, we design a MEC platform with heterogeneous MIoTDs participating in a computational microservice offloading scheme. Here, we propose an incentive approach applying a double auction mechanism to incentivize the involvement of MIoTDs. In practice, the incentive mechanism typically interacts with the demand estimation scheme that estimates the demand profile of MIoTDs. As a result, we design a novel mechanism for microservices - microservice Incentive Service Offloading (mISO), which comprises an incentive approach and a demand estimation scheme. The mISO mechanism holds truthfulness, rationality, and low computational complexity while guaranteeing positive social welfare and generating the optimal demand profiles for MIoTDs. Simulation results showed that mISO provides 18-21$\%$% and 25-30$\%$% improvements in terms of average latency and resource utilization compared to existing works. © 2008-2012 IEEE.