In this paper, a game theoretic approach is used to derive the optimal power allocation in multiple access channels (MAC) for decentralized systems. Unlike previous results, a simple coordination mechanism is used between selfish users. The nature and influence of the coordination mechanism is studied in details for single antenna and multiple antenna terminals. In the proposed framework, the coordination signal indicates to the users in which order the receiver applies successive interference cancelation and with which frequency this order is used: it establishes the rule of the game. Remarkably, in Gaussian single input single output MACs, it is shown that, whatever the rule of the game, the selfish behavior of the users leads to a socially efficient network that is to say it is always sum-capacity achieving. However, for fast fading MAC with multi-antenna terminals, there can be a performance gap between the decentralized system and its centralized counterpart. Analytical and simulation results are provided to assess this gap.