Detailed research focusing on the inter-cluster routing for wireless sensor networks (WSNs) is given first. The energy consumption imbalance problem and its cause are presented through a simple example. The paper points out the fact via an example that

the selfish of each cluster head leads to the imbalanced distribution of data flow and the data distribution imbalance then results in energy consumption imbalance. Subsequently

the non-cooperative game model aiming at regulating the behavior of the cluster heads is proposed. The Nash Equilibrium Point (NEP) of the game model is then obtained and proved. According to this game model

an energy-efficient Inter-cluster Routing algorithm based on Non-cooperative Game (EIRNG) is presented

which is the key contribution of the paper. Finally

extensive simulation experiments are conducted and the horizontal and vertical contrast in terms of energy efficiency and network performance are also made. The results show that the cluster heads tend to dissipate energy evenly via determining the optimal amount of the traffic based on a balance factor θi. Compared with the classic clustering routing PEGASIS and the authors' former work EEREG

the network lifespan can be extended by 74.1% and 8.6% respectively. Therefore

the proposed EIRNG can improve the energy efficiency and the network performance of the network effectively.