In this paper, we envisage the architecture of Green Wireless Body Area Nano-network (GBAN) as a collection of nano-devices, in which each device is capable of communicating in both the molecular and wireless electromagnetic communication modes. The term green refers to the fact that the nano-devices in such a network can harvest energy from their surrounding environment, so that no nano-device gets old solely due to the reasons attributed to energy depletion. However, the residual energy of a nano-device can deplete substantially with the lapse of time, if the rate of energy consumption is not comparable with the rate of energy harvesting. It is observed that the rate of energy harvesting is non-linear and sporadic in nature. So, the management of energy of the nano-devices is fundamentally important. We specifically address this problem in a ubiquitous healthcare monitoring scenario and formulate it as a cooperative Nash Bargaining game. The optimal strategy obtained from the Nash equilibrium solution provides improved network performance in terms of throughput and delay.