Deploying Federated Learning within blockchain is widely adopted due to its ability to leverage decentralized architecture to ensure security and privacy while facilitating the allocation of training rewards. However, in real-world scenarios, an unreasonable incentive mechanism may lead to clients’ reluctance to participate in training due to insufficient or unfair reward distribution. Furthermore, clients might adopt abnormal training strategies that negatively impact the final model performance for reduced costs or additional gain. Thus, designing a fair and robust incentive model that promotes continuous and honest participation remains a significant challenge. In this paper, we propose a game-theoretic dynamic incentive model termed FRFL, which allocates rewards based on client contributions and reputation. The model incentivizes honest participation by introducing a game theory-based reward distribution strategy. By analyzing payoffs for bounded rationality clients under various conditions, we calculate the Sequential Equilibrium and the Evolutionarily Stable Strategy (ESS) to assess model stability and demonstrate through simulations that our model successfully converts participants employing unconventional strategies into honest participants, thereby ensuring system robustness.