Decentralized learning, a paradigm enabling the training of Machine Learning (ML) models using multiple nodes, is gaining momentum, as it (i) improves data privacy and (ii) permits to leverage the computational capabilities of a wide set of nodes, thus being an excellent fit for the support of edge intelligence applications. However, such nodes, like users’ smartphones or vehicles, cannot be forced to participate in the learning process, and incentivizing them to do so is one of the foremost challenges of decentralized learning. To address this issue, we propose GENIAL – a game-theoretic approach, based upon generous games, to promote cooperation among user nodes for training or fine-tuning ML models. By allowing such nodes to be (moderately) generous, i.e., to contribute to decentralized training processes more often than what would be convenient for them in the short term, GENIAL leads to a Nash equilibrium where all nodes cooperate. Importantly, such equilibrium is also proven to converge to the Pareto optimal operating point that ensures a fair treatment to all nodes. Our theoretical findings are supported by numerical experiments, which further underline the effectiveness, and the benefits for rational nodes, of being generous in decentralized training.