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The call admission control (CAC) for mobile multimedia communications is one of the most important engineering issues since it belongs to the category of resource management and the radio spectrum is a very scarce resource. As efficiency is an important performance issue in the mobile networks with multimedia services, the concept of fairness should also be considered. In this paper, a selection of guard bandwidth coefficients of the CAC scheme for the asymmetrical traffic case in mobile multimedia communications based on the framework of game theory is proposed. Class 0 calls and class 1 calls are viewed as two players of a game. The proposed scheme provides fair and efficient resource allocation for the 2 classes of traffic, and also guarantees the priority of class 0 calls over class 1 calls. The numerical results show that the equilibrium point of the noncooperative game is similar to the solutions of both of the interpersonal comparisons of utility and the bargaining problem for the cooperative game. Moreover, the way to generate the Pareto boundary is demonstrated. Hence, the Nash solution of the bargaining problem can be obtained easily. The numerical results also show that the Nash solution with the origin (0,0) as the starting point can achieve higher total utilization than that of the equilibrium point.