Cooperative communication has been studied as a way to improve reliability of networks compared to conventional direct transmission scheme. We consider amplify-and-forward (AF) cooperative communication with multiple relays. In this system, there is a problem that which relay nodes should be selected and how much power should be allocated to the selected relay nodes. Most of conventional researches on this model have focused on only improving channel capacity or reliability, rather than saving power consumption in all over the network with maintaining such communication qualities. In this paper, we propose a new power allocation scheme for multiple relay nodes using game theory that focuses on transmission power efficiency. With computer simulation, we show that our proposed game theoretical approach has superiority to some conventional schemes from the viewpoint of transmission power efficiency.