For the sake of protecting data privacy and due to the rapid development of mobile devices, e.g., powerful central processing unit (CPU) and nascent neural processing unit (NPU), collaborative machine learning on mobile devices, e.g., federated learning, has been envisioned as a new AI approach with broad application prospects. However, the learning process of the existing federated learning platforms rely on the direct communication between the model owner, e.g., central cloud or edge server, and the mobile devices for transferring the model update. Such a direct communication may be energy inefficient or even unavailable in mobile environments. In this paper, we consider adopting the relay network to construct a cooperative communication platform for supporting model update transfer and trading. In the system, the mobile devices generate model updates based on their training data. The model updates are then forwarded to the model owner through the cooperative relay network. The model owner enjoys the learning service provided by the mobile devices. In return, the mobile devices charge the model owner certain prices. Due to the coupled interference of wireless transmission among the mobile devices that use the same relay node, the rational mobile devices have to choose their relay nodes as well as deciding on their transmission powers. Thus, we formulate a Stackelberg game model to investigate the interaction among the mobile devices and that between the mobile devices and the model owner. The Stackelberg equilibrium is investigated by capitalizing on the exterior point method. Moreover, we provide a series of insightful analytical and numerical results on the equilibrium of the Stackelberg game.