This paper deals with the cross-layer design of a decentralized medium access control (MAC) scheme to coordinate the access of multiple transmitters adopting a Multi-Packet Reception (MPR) physical (PHY) layer. Knowing that in MPR systems the average number of packets successfully decoded depends on the number of simultaneous transmissions, we propose an integrated PHY/MAC cross-layer design that explores the advantages of MPR communications in a decentralized network. The joint performance of the PHY/MAC cross-layer scheme is characterized to allow the maximization of the average number of packets successfully decoded. While the main objective of the proposed MAC is to randomly grant access to the channel in order to achieve the optimal number of simultaneous transmissions, the decentralized MAC introduces a cost due to the time required to coordinate the multiple transmitters. In a first step we characterize the throughput achieved by the cross-layer scheme, by modeling the performance of the PHY-layer and the random MAC scheme. The formal characterization of the throughput is then used to optimize the duration of the first stage of the MAC scheme. In this way, the number of transmitters is regulated to optimize the cross-layer operation, taking into consideration the features of the MPR PHY-layer and the maximum performance achieved with the proposed MAC design. Several results obtained through simulation are presented, which validate the numerical results obtained with the proposed characterization. Finally, the results confirm the advantages of the proposed PHY/MAC design.