Multi-player evolutionary game of federated learning incentive mechanism based on system dynamics

Federated learning has emerged as a new way of data sharing. The participants in the federation tend to choose different strategies based on their benefits, which is formalized into an evolutionary game model. Existing techniques can limit the malicious behavior of participants by detecting betrayers or weakening their influence. The problem that whether there is an incentive mechanism which makes participants spontaneously choose to cooperate honestly and maintains the stability of the federated learning system is urgent. In this paper, we develop a multi-player evolutionary game model in federated learning. We model the federated learning process by evaluating the payoffs of the central server, internal clients, and external clients. The stability of the federated learning system in the long-term dynamics process is assessed by seeking the evolutionarily stable equilibrium solutions. In this paper, mathematical reasoning and computer simulation are combined to analyze the impact of reward and punishment strategies in incentive mechanisms on the game process and game equilibrium. An incentive mechanism is designed to achieve evolutionarily stable equilibrium while make most clients join the federation spontaneously and cooperate honestly. Finally, the effectiveness, stability, and generalizability of this incentive mechanism are verified by sensitivity analysis and Lyapunov stability theory.