Simultaneously information and power transfer in mobile relay networks have recently emerged, where the relay can harvest the radio frequency (RF) energy and then use this energy for data forwarding and system operation. Most of the previous works do not consider that the relay may have its own objectives, such as using the harvested energy for its own transmission instead of maximizing transmission of the network. Therefore, in this paper, we propose a Nash bargaining approach to balance the information transmission efficiency of source-destination pairs and the harvested energy of the relay in a wireless powered relay network with multiple source-destination pairs and one relay. We analyze and prove that the Nash bargaining problem has several desirable properties such as the discreteness and quasi-concavity, when it is decomposed into three sub-problems: the energy transmission power optimization, the power control for data transmission and the time division between energy transmission and data transmission. Based on the theoretical analysis, we propose an alternating power control and time division algorithm to find a suboptimal solution. Simulation results clearly show and demonstrate the properties of the problem and the convergence of our algorithm.