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In order to find a stable-aware way in view of load sharing and routing stability to split traffic load over multi-path, we develop a traffic assignment for multi-path routing in cognitive radio ad hoc networks in this paper. In the framework of game theory, the problem coincides with a n-person noncooperative differential game. We show that the feedback Nash equilibrium of the game is a stableaware traffic assignment. We also carry out some numerical experiments to illustrate the influence of game parameters on traffic assignment.