关键词: 无线传感器网络（WSN）, 拓扑控制, 势博弈, 纳什均衡

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