Clustering is known to be an effective means of reducing energy dissipation and prolonging network lifetime in wireless sensor networks (WSNs). Recently, game theory has been used to search for optimal solutions to clustering problems. The residual energy of each node is vital to balance a WSN, but was not used in the previous game-theory-based studies when calculating the final probability of being a cluster head. Furthermore, the node payoffs have also not been expressed in terms of energy consumption. To address these issues, the final probability of being a cluster head is determined by both the equilibrium probability in a game and a node residual energy-dependent exponential function. In the process of computing the equilibrium probability, new payoff definitions related to energy consumption are adopted. In order to further reduce the energy consumption, an assistant method is proposed, in which the candidate nodes with the most residual energy in the close point pairs completely covered by other neighboring sensors are firstly selected and then transmit same sensing data to the corresponding cluster heads. In this paper, we propose an efficient energy-aware clustering protocol based on game theory for WSNs. Although only game-based method can perform well in this paper, the protocol of the cooperation with both two methods exceeds previous by a big margin in terms of network lifetime in a series of experiments.