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We investigate a data quality-aware dynamic client selection problem for multiple federated learning (FL) services in a wireless network, where each client offers dynamic datasets for the simultaneous training of multiple FL services, and each FL service demander has to pay for the clients under constrained monetary budgets. The problem is formalized as a non-cooperative Markov game over the training rounds. A multi-agent hybrid deep reinforcement learning-based algorithm is proposed to optimize the joint client selection and payment actions, while avoiding action conflicts. Simulation results indicate that our proposed algorithm can significantly improve training performance.