Fog computing is a distributed architecture which extends cloud computing resources to the end user. Furthermore, fog computing is deployed increasingly to fulfill the requirements of the Internet of Object (IoT) technology. This solution has been proposed to overcome the shortcomings of the cloud. Motivated by recent advances in fog computing, we aim to improve the performances of fog-cloud systems. A novel system design is proposed in which the energy consumption and the delay are considered. Different queue models are applied to our system, where the energy and delay costs are modeled. A coalition game between fog nodes is formulated to minimize the cost, while examining the energy-delay trade-off. To this end, we propose three energy-efficient solutions with the objective of minimizing the total cost of the execution of IoT applications in a fog-cloud system. Our simulation shows the effectiveness of the proposed solutions compared to works from the literature.