We present a team analysis of a slotted random wireless channel access mechanism. Under the proposed scheme, denoted wireless random access mechanism with multiple power levels (MPL-WRA), each mobile station contends for a transmission opportunity following the principles of a slotted access mechanism incorporating a random transmitting power value selected among various available power levels. In this way, a capture effect may be produced allowing the packet to be decoded whenever the signal-to-interference-plus-noise ratio is higher than a given threshold. In order to analyze the performance and optimization of the proposed setup, we build a Markovian model integrating the wireless access mechanism supplemented by the use of multiple power levels in an attractive and simple cross-layer fashion. We follow a team problem approach allowing us to fine tune the design parameters of the overall system configuration. Throughout an extensive numerical analysis, our main results set the basis for the social optimal system configuration of the proposed mechanism taking into account the physical constraints of using multiple power levels and the actual practical implementation of a slotted access mechanism. We end the paper with concluding remarks and future research directions including guidelines for the actual implementation of our proposal. © 2013 Abdelillah Karouit et al.