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