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Inspired by the shared infrastructure of colocation data centers and the growth of Mobile Edge Computing (MEC), colocation MEC businesses have thrived to offer an economical and low latency solution for MEC based tenants. In colocation MEC, a colocation service provider leases spaces at the base stations (BSs) to tenants for housing their servers. Although the tenants fully manage their own servers, they still need to purchase bandwidth from the network provider to via bandwidth purchasing market to serve their users. As a result, tenants should consider the trade-off between delay and energy consumption, which are related to bandwidth and server computing speed, respectively. In this paper, an auction framework is used to model the interaction between the network provider and tenants in the bandwidth market. The network provider determines the bandwidth amount and corresponding payment by tenants based on their submitted bids, in which the valuation of the bandwidth amount in each bid is based on the coupling between bandwidth and server computing speed. The networking provider also seeks winners in the social welfare maximization problem, which is NP-hard. To solve this problem, we propose a solution based on the randomized auction mechanism, which is proved to be approximately truthful, individually rational, and computationally efficient. Simulation results verify the effectiveness of our proposed randomized auction scheme in bandwidth trading. [ABSTRACT FROM AUTHOR]