A game theoretic method was proposed to adaptively maintain the energy efficiency in distributed wireless sensor networks. Based on a widely used transmission paradigm, the utility function was formulated under a proposed noncooperative framework and then the existence of Nash Equilibrium (NE) has been proved to guarantee system stability. To pursuit NE, an NPC algorithm was proposed to regulate heterogeneous nodes with various communication demands given the definition of urgency level. Results from both simulation and real testbed presented the robustness and rapid convergence of NPC algorithm. Furthermore, the network performance can remain in a promising state while the energy consumption is greatly decreased. 1. Introduction Power control is one of the critical issues in wireless sensor networks (WSNs), especially when node is battery-powered. In wireless network, both throughput and bit error rate (BER) depend on the signal to interference and noise ratio (SINR) on receiver side, which will result in the transmission dilemma in wireless sensor networks. If transmitter raises its transmission power to increase SINR, it will inevitably also act as noise to other nodes which are on the same channel. Therefore, power control in WSNs has been targeting to find certain appropriate strategies to alleviate the effect. Most of solutions focus on regulating transmission power to increase the network capacity and prolong the battery life. To better manipulate transmitter power, Yates proposed an analytic method for power iteration, which is based on the satisfaction of signal to interference ratio (SIR) requirement [1]. A SIR balancing algorithm was developed by Zander that each and every terminal, by using this algorithm, would periodically adjust their power to converge to the corresponding SIR equilibrium [2]. As wireless sensor network has been evolving as the popular platform for large-scale applications, an alternative approach to the power control problem based on the game theory has been discussed. For example, in military and emergency scenarios, wireless sensor nodes under the same authority tend to work with each other in a fully cooperative way. Wu et al. proposed a fill-fledged cross-layer optimization design, which operated in a bandwidth-limited regime and in an energy-limited regime. The significant performance could be achieved by making a tradeoff between throughput and energy efficiency [3]. Wu and Bertsekas pointed out that generally power levels are assigned from a discrete set, and each mobile node holds its own interest so that the
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