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The rapidly growing demand for wireless communication makes efficient power allocation a critical factor in the network's efficient operation. Power allocation in decentralized wireless systems, where the transmission of a user creates interference to other users and directly affects their utilities, has been recently studied by pricing methods. However, pricing methods do not result in efficient/optimal power allocations for such systems for the following reason. Systems where a user's actions directly affect the utilities of other users are known to have externalities. It is well known from Mas-Colell that in systems with externalities, standard efficiency theorems on market equilibrium do not apply and pricing methods do not result in Pareto optimal outcomes. In this paper, we formulate the power allocation problem for a wireless network as an allocation problem with ??externalities.?? We consider a system where each user knows only its own utility and the channel gains from the transmitters of other users to its own receiver. The system has multiple interference temperature constraints to control interference. We present a decentralized algorithm to allocate transmission powers to the users. The algorithm takes into account the externality generated to the other users by the transmission of each user, satisfies the informational constraints of the system, overcomes the inefficiency of pricing mechanisms and guarantees convergence to globally optimal power allocations.