We consider a multiple access channel where the users choose their best power control strategy in order to sel¯shly max- imize their energy-e±ciency. To increase the utilities with respect to the classical non-cooperative game, we introduce hierarchy in two ways. On the one hand, assuming single- user decoding at the receiver, we investigate a Stackelberg formulation of the game where one user is the leader. On the other hand, assuming neither leader nor followers among the users, we introduce hierarchy by using successive in- terference cancelation at the receiver. For both cases, we study the existence and uniqueness of an equilibrium and compare the individual performance obtained in the hierar- chical game with that obtained in the non-cooperative game. An exhaustive comparative analysis of the two games is also conducted. In order to optimize the choice of the leader in the Stackelberg formulation (with single user decoding) and that of the decoding order (in the non-cooperative game with successive interference cancelation), we study two measures of global energy-e±ciency for the network and discussions are provided for each case.