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This paper presents a game theoretic approach to the routing of multiple real-time multimedia streams through multiple shared links with different link quality metrics. The objective of the proposed method is to achieve fairness and bandwidth efficiency for each stream in the utilization of high quality links. Traditionally this task is managed through pricing and service agreement, and the solutions are frequently sub- optimal. In this paper, the problem of path link sharing among multiple streams is formulated as a non-corporative QoS game. Each stream is a player, whose strategy space is the percentage of utilization of the high quality links. A unique payoff function is introduced, and each player attempts to maximize its expected payoff independently. The existence and uniqueness of a Nash equilibrium (NE) is analyzed. Numerical experiments are conducted, and the results demonstrate that the NE solutions are optimal in maximizing the successful transmission of individual streams.