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Aiming at both prolonging the lifetime of the networks and decreasing the end-to-end delay of the networks, we apply GSP (generalized second price) auction game to the problem of joint bandwidth allocation and routing in low-medium-altitude platforms-based PMP/Mesh networks. In the paper, this problem is first modeled as GSP auction game. To decrease the computation overhead of resolving algorithm, the algorithm based on fuzzy particle swarm optimization is then presented. Extensive evaluations show that compared to the other two typical auction-based routing and bandwidth allocation algorithms, that is, least cost path algorithm and AODV with auction algorithm, the proposed algorithm not only achieves a good trade-off between average end-to-end delay and the lifetime, but also a good percentage of dropped packets.