Abstract: Federated learning (FL) has emerged as a powerful scheme to facilitate the collaborative learning of models amongst a set of agents holding their own private data. Although the agents benefit from the global model trained on shared data, by participating in federated learning, they may also incur costs (related to privacy and communication) due to data sharing. In this paper, we model a collaborative FL framework, where every agent attempts to achieve an optimal trade-off between her learning payoff and data sharing cost. We show the existence of Nash equilibrium (NE) under mild assumptions on agents' payoff and costs. Furthermore, we show that agents can discover the NE via best response dynamics. However, some of the NE may be bad in terms of overall welfare for the agents, implying little incentive for some fraction of the agents to participate in the learning. To remedy this, we design a budget-balanced mechanism involving payments to the agents, that ensures that any $p$-mean welfare function of the agents' utilities is maximized at NE. In addition, we introduce a FL protocol FedBR-BG that incorporates our budget-balanced mechanism, utilizing best response dynamics. Our empirical validation on MNIST and CIFAR-10 substantiates our theoretical analysis. We show that FedBR-BG outperforms the basic best-response-based protocol without additional incentivization, the standard federated learning protocol FedAvg, as well as a recent baseline MWFed in terms of achieving superior $p$-mean welfare.