Due to resource constraints and severe conditions, wireless sensor networks should be self-adaptive to maintain certain desirable properties, such as energy efficiency and fault tolerance. In this paper, we design a practical utility function that can effectively balance transmit power, residual energy, and network connectivity, and then we investigate a topology control game model based on non-cooperative game theory. The theoretical analysis shows that the topology game model is a potential game and can converge to a state of the Nash equilibrium. Based on this model, an energy-efficient and fault-tolerant topology control game algorithm, EFTCG, is proposed to adaptively constructs a network topology. In turn, we present two subalgorithms: EFTCG-1 and EFTCG-2. The former just guarantees network single connectivity, but the latter can guarantee network biconnectivity. We evaluate the energy-efficient effect of EFTCG-1. Meanwhile, we also analyze the fault-tolerant performance of EFTCG-2. The simulation results verify the validity of the utility function. EFTCG-1 can efficiently prolong the network lifetime compared with other game-based algorithms, and EFTCG-2 performs better in robustness, although does not significantly reduce the network lifetime.
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