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The paper considers the problem of joint assignment of bandwidth and route in multi-path selfish networks. We model this problem as auction game and make mechanism design. The model is a convex optimization problem, and large computation overhead is needed to resolve it. We make theoretical analysis and present two algorithms to resolve the model. One is hybrid water filling assignment algorithm for non-linear cost function, and the other is Least-Cost-Path-based assignment algorithm for linear cost function. Extensive evaluations show that these two algorithm can decrease computation overhead and the second also decrease the total cost of participant nodes.