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How to allocate rate to users with multiple services efficiently and fairly is an important issue in the wireless network. To ensure the quality of service required by multiple services of a user, efficient resource management becomes paramount. On the other hand, the fairness between users is also necessary. In this paper, we propose a bandwidth allocation scheme named as Efficiency and Inter-user Fairness (EIF). In the EIF scheme, the well-known game theoretic concept of Nash bargaining solution is deployed to allocate the total network bandwidth to users fairly and dispatch rate from user to services efficiently by maximizing the user's utility. We also propose a distributed algorithm for implementing the convex optimization problem in the EIF scheme. Simulation results show that the EIF scheme outperforms the compared schemes in that it considers both the system efficiency and the user's fairness, while other schemes only maximizes the total utility of all of the services or considers the user's fairness.