We investigate the achievable performances of multi-carrier energy efficient power control game. Both the simultaneous-move and the hierarchical games are addressed. For the first time, we derive analytical closed-form expressions of the spectrum coordination and the spectral efficiency of such models. Our results indicate that the spectrum coordina-tion capability induced by the power control game model enables the wireless network to enjoy the energy efficiency improvement while still achieving a high spectral efficiency. Such an important result offers insights into how to design power control in multi-carrier radio environments.