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Medium access control (MAC) protocol design for cooperative networks over multi-packet reception (MPR) channels is a challenging topic, but has not been addressed in the literature yet. In this paper, we propose a cooperative multi-group priority (CMGP) based MAC protocol to exploit the cooperation diversity for throughput enhancement over MPR channels. The proposed approach can bypass the computationally-intensive active user identification process. Moreover, our method can efficiently utilize the idle periods for packet relaying, and can thus effectively limit the throughput loss resulting from the relay phase. By means of a Markov chain model, the worst-case throughput analysis is conducted. The results allow us to investigate the throughput performance of the proposed CMGP protocol directly in terms of the MPR channel coefficients. Simulation results confirm the system-wide throughput advantage achieved by the proposed scheme, and also validate the analytic results.