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Successive Interference Cancellation (SIC) is a physical-layer technique that enables reception of multiple overlapping transmissions. While SIC has the potential to boost the network throughput, if the MAC protocol employed in the network is agnostic to such a capability at the physical-layer, the full potential of SIC can not be utilized in the network. There have been a number of studies to design new SIC-aware MAC protocols or adjust the existing protocols to exploit SIC. Despite that, the exact effect of MAC protocols on the throughput of SIC-enabled networks is unknown. In this paper, we propose a novel SIC-aware MAC protocol based on the disparity of user channels in a wireless network and analyze its performance. We consider a simple random access protocol with no SIC as the base configuration and compare it with three other configurations with different levels of SIC-awareness. We show that while a SIC-enabled physical layer without a SIC-aware MAC protocol can increase the throughput of the network by 1.5×, a specifically designed MAC protocol is far more efficient achieving up to 3.3× improvement in throughput. Our SIC-aware MAC protocol is fully distributed and hence subject to selfish behavior of users. Thus, we also consider the case where the users behave selfishly. We model our proposed protocol as a one-shot simultaneous move game and derive a mixed strategy Nash equilibrium. We also show that we can set the cost of packet transmission in such a way that we get the optimal system throughput at the Nash equilibrium.