While mobile edge computing (MEC) holds promise to enhance users' mobile experience, how to make appropriate offloading decisions under consideration of quality of service (QoS) and energy consumption requirements is challenging. In this research, we focus on obtaining an equilibrium solution that ensures not only the fairness of terminal users and utility maximization for the edge service providers but also QoS and energy consumption requirements. We formulate the cooperative game resource allocation optimization problem (CGRA) under the complete/incomplete information environment and propose the Nash Bargaining Cooperative Game (NBCG) policy to solve it. We perform experiments and compare it with six schemes. Experimental results show that the proposed NBCG can gain better offloading profits than the benchmarks and improve the percent of guaranteed tasks by as much as 23% under different input data sizes, as much as 18% under different time delay tolerances, and as much as 25% under different execution weights.