Data offloading to Mobile Edge Computing (MEC) servers is an attractive choice for resource-constrained Internet of Things (IoT) devices, towards reducing their computational effort. In this paper, we investigate the potential of partial data offloading to MEC servers, under the perspective of users' cognitive IoT devices presenting loss averse and gain seeking behavior. Due to the sharing nature of the access environment and the MEC server's computational characteristics, we treat the MEC server option as a common pool of resources with uncertain payoff returned to the users, while the local computation capability is treated as a safe option for each user. Following the properties of Prospect Theory, users' prospect-theoretic utilities are formulated exploiting the local computing and offloading overhead options under probabilistic uncertainty. Such a modeling allows for the infusion of human awareness, inherent cognitive biases and behavioral characteristics into the devices' operation, their data offloading decisions and the edge computing environment that the devices are interacting with. Accordingly, each user's optimal offloaded data to the MEC server is obtained as the outcome of a non-cooperative game, with users attempting to maximize their own utilities. The existence and uniqueness of a Pure Nash Equilibrium (PNE) are proven under the probabilistic nature of the respective payoff functions, while a distributed algorithm that convergences to the PNE is designed. Numerical results are provided that demonstrate the operation and superiority of the proposed framework under different IoT scenarios and behaviors, considering both homogeneous and heterogeneous users. INDEX TERMS Intelligent data offloading, mobile edge computing, Internet of Things, risk-based behavior modeling, cognitive decision making, probabilistic uncertainty.