Commercial deployment of 4G LTE networks and rapid penetration of smart phones have exponentially increased the wireless data traffic, thus increasing the energy consumption and greenhouse (CO2) gas emission. The concept of green 4G LTE networks lies in the development of energy efficient LTE systems for reducing the greenhouse emissions as well as operators’ energy bill. In this letter we first identify the complexity of the optimal traffic awareness in LTE networks and subsequently design a cooperative communication framework for traffic-aware energy optimization. The LTE eNBs explore an information theoretic approach to capture the dynamics and uncertainty of network traffic. Subsequently, using an online, stochastic game theoretic algorithm, the eNBs communicate amongst themselves to optimize the traffic awareness. Optimal traffic awareness helps in reducing the network energy consumption. Simulation results demonstrate that our framework results in almost 22% (40 KWHr) daily energy savings across a LTE network of 400 cells.