Incentive mechanisms are crucial for motivating participants to make significant contributions to Federated Learning (FL). However, most existing works focused on incentive mechanisms considering only a single model owner, despite the fact that collaboration among multiple model owners can lead to the training of more robust and accurate models. Additionally, fairness is essential for ensuring sustainable participation in the training process. In this paper, we propose a gme-theoretic fair incentive mechanism (GAIN) to motivate cooperation among multiple model owners and edge devices by providing them with a fair distribution of benefits. Specifically, we model the edge device selection problem as a multi-leader multi-follower Stackelberg game, prove the monotonicity of the selection process, and derive the Stackelberg equilibrium (SE) through rigorously designed algorithms. We model the cooperation process among multiple model owners as a coalition game to maximize social utility. Moreover, We introduce the \(\rho \) -Lipschitz condition as a fair criterion to design transfer payments, thereby enhancing the enthusiasm of model owners and further increasing social utility. Experimental performances on simulated and real-world datasets demonstrate that our mechanisms outperform the state-of-the-art baselines, achieving improvements of 32.1% in social utility and 6.3% in test accuracy.