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A cooperative bandwidth and power allocation algorithm is presented for multi-relay based networks. All the relays adopt the decode-and-forward protocol and assist the transmission from the source to destination in a non-cooperative game. By using a utility based mechanism, two types of resource allocation algorithms, namely bandwidth and power allocation strategy are proposed so as to maximize the source's utility. Specifically, we first developed the optimal bandwidth allocation schemes under equal power allocation assumption among relays. Then, we considered the optimal power and bandwidth allocation for the multi-relay cooperative transmission subject to individual power constraints on the source. Simulation studies are conducted to evaluate the effectiveness of the proposed algorithms in terms of utility. The impact of the proposed strategy on power and bandwidth allocation is also discussed.