The problem of cooperative spectrum leasing to unlicensed Internet of Things (IoT) devices is studied to account for potential selfish behavior of these devices. A distributed game theoretic framework for spectrum leasing is proposed where the licensed users can willingly lease a portion of their spectrum access to unlicensed IoT devices, and in return the IoT devices provide cooperative services, firstly to enhance information secrecy of licensed users via adding intentional jamming to protect them from potential eavesdroppers, and secondly to enhance the quality of communication through cooperative relaying. The cooperative behavior of the potentially selfish IoT devices is monitored using a reputation-based mechanism to enable the primary users to only interact with the reliable IoT devices. The simulation results show that using the proposed reputation-based method enhances the secrecy rate of the primary users by reducing the possibility of attacks from selfish IoT devices. Hence, this model can offer a practical solution for spectrum leasing with mobile IoT devices when assuring the required quality of communication and information secrecy for the spectrum owners.