Abstract: Since the energy of sensor node is limited, and node is not easily replaced, energy efficiency issue has been an important factor that restricting sensor network lifetime. This paper constructs a topology control algorithm based on a potential game (potential game topology control, PGTC), and takes the smallest potential lifetime and degree respectively as primary and secondary utility functions. By adjusting transmitting power, nodes reduce the power of the node which has the shortest potential lifetime in reverse-link set to extend its potential lifetime, while controlling the node degree to reduce the average hops of link and total energy consumption. This paper analyzes that the PGTC model is an ordinal potential game and possesses a Nash equilibrium which is Pareto optimal. The simulation results indicate that the PGTC algorithm reduces the total energy consumption of network and the difference in energy between nodes compared with other topology control algorithms based on game theory.

Key words: wireless sensor network (WSN), topology control, potential game, Nash equilibrium

摘要： 由于传感器节点能量有限且不易更换，故能量效率一直是制约传感网生存周期的重要因素。构建一种基于势博弈的拓扑控制（potential game topology control，PGTC）模型，将最短潜在寿命和节点度取值分别作为首要、次要效用函数。节点调整自身的发射功率，降低反向链路集中潜在寿命最短节点的发射功率，延长其潜在寿命，同时控制节点度取值以减小链路平均跳数和总能耗。理论分析可知，PGTC模型属于序数势博弈，存在纳什均衡，且纳什均衡点即为帕累托最优解。仿真表明，PGTC模型相较于其他基于博弈论的拓扑控制算法，网络总能耗更低，并且能量均衡性更强。

关键词: 无线传感器网络（WSN）, 拓扑控制, 势博弈, 纳什均衡