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In this paper, a simple decentralized power allocation strategy is proposed, which relies on the local information in a single-hop wireless network with n links. The main goal of the strategy is to improve the average sum-rate. We first define a new utility-based framework, in which each user takes into account the negative impact of its power increment on the other users performance. For large n and by knowing only the direct channel gain hii, the optimum strategy for user i is to transmit with full power or remain silent. The transmission policy is to compare hii with a prespecified threshold taun that is a function of n. Under a Rayleigh fading channel condition, it is demonstrated that among n pairs of nodes, the average number of active links is of order log n. Also, the average sum-rate scales as Theta(log n). The performance of the proposed strategy is compared with that of the centralized power allocation scheme and the non-cooperative power control games through simulation and the analytical arguments. The proposed on-off power allocation scheme has the advantage of not requiring a central controller. The proposed strategy relies on a one shot game with a simple structure, rather than the iterative mechanism used in the pricing algorithm. These properties make our scheme more practical in time-varying networks.