To address the issues of delayed reputation updates, lack of incentive mechanisms, and insufficient cooperation stability in traditional Raft consensus under consortium blockchain environments, this study proposes the reputation and game-theoretic enhanced Raft (RGE-RAFT) algorithm. A Markov-based reputation evolution model is introduced to dynamically quantify node behavior. A repeated game mechanism is incorporated, and a reward-penalty function is used to guide long-term cooperation among nodes. The leader election adopts a reputation-weighted probabilistic strategy with a cooling factor, preventing high-reputation nodes from long-term monopoly and improving fairness and decentralization. Theoretical analysis shows that the system reputation state converges to a unique steady state, and node strategies reach a subgame perfect equilibrium. Experimental results demonstrate that in a 60-node scenario, the throughput of RGE-RAFT increases by approximately 23.7% compared with Raft, 12.2% compared with T_Raft, and 5.1% compared with K-Raft, while the average consensus latency decreases by about 12.9%. Node reputation values converge within a finite number of rounds, forming stable hierarchical layers. Superior performance is also achieved in terms of leader election fairness and system stability. The results indicate that the integration design of reputation-driven consensus and self-incentivized game in RGE-RAFT provides a new approach for constructing stable and trustworthy consortium blockchain consensus mechanisms.