In wireless sensor networks, nodes may adopt selfish behavior to save their energy resources, which causes energy imbalance among nodes, because of lacking a central controller with the function of making nodes cooperate. Noncooperative game is an effective tool for portraying this kind of selfish behavior. In this paper, we address the problems of transmission power minimization and energy balance using a topology control game. Firstly, we establish a topology control game model and prove that the topology game model is an ordinal potential game with Pareto optimality. Secondly, based on this model, we propose an Energy Balance Topology control Game algorithm (EBTG), in which, by taking the energy efficiency and energy balance of the nodes into account, we design an improved optimization-integrated utility function by introducing the Theil index. Finally, simulation results show that the EBTG algorithm can improve the energy balance and energy efficiency, and can prolong the network lifetime in comparison with other topology control algorithms based on game theory.
Keywords: energy balanced; game theory; topology control; wireless sensor networks.