This paper investigates the relay assignment and power allocation problem for two different network power management policies: group lifetime maximization (GLM) and minimum weighted total power (MWTP), with the aim of lifetime maximization in symbol error rate (SER) constrained multipleuser cooperative network. With optimal power allocation solution obtained for each policy, we show that the optimal relay assignment can be obtained using bottleneck matching (BM) algorithm and minimum weighted matching (MWM) algorithm for GLM and MWTP policies, respectively. Since relay assignment with BM algorithm is not power efficient, we propose a novel minimum bottleneck matching (MBM) algorithm to solve the relay assignment problem optimally for GLM policy. To further reduce the complexity of the relay assignment, we propose suboptimal relay selection (SRS) algorithm which has linear complexity in number of source and relay nodes. Simulation results demonstrate that the proposed relay selection and power allocation strategies based on GLM policy have better network lifetime performance over the strategies based on MWTP policy. Compared to the MBM and SRS algorithm, relay assignment based on BM algorithm for GLM policy has inferior network lifetime performance at low update interval. We show that relay assignment based on MBM algorithm achieves maximum network lifetime performance and relay assignment with SRS algorithm has performance very close to it.