Clustering has been known as an effective way to reduce energy dissipation and prolong network lifetime in wireless sensor networks (WSNs). Game theory (GT) has been used to find the optimal solutions to clustering problems. However, the residual energy of nodes is not considered when calculating the equilibrium probability in the earlier studies. Besides, under the perspective of energy consumption, the definitions of payoffs in local clustering games are required when calculating the equilibrium probability. Based on the considerations, a hybrid of the equilibrium probability attained by playing local clustering games and a cost-dependent exponential function is proposed to get the probability to be CH(Cluster Head), in which new definitions of payoffs under the perspective of energy consumption are used. In the paper, we proposed an efficient distributed, gametheory based clustering protocol (EDGC) for Wireless Sensor Networks. Simulation results show that the proposed clustering protocol EDGC outperforms LEACH, LGCA and HGTD in terms of network lifetime.