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This paper considers a wireless network where users cooperate with each other to improve the network performance. Our goal is to design an optimal power allocation algorithm for user cooperation in a distributed fashion. We formulate the power allocation problem as a multi-auctioneer multi-bidder power auction. Specifically, each user acts as both an auctioneer (seller) and a bidder (buyer). Each auctioneer independently determines its trading price and allocates power to bidders, and each bidder chooses the demand from each auctioneer. We show that there exist bidding and pricing strategies that maximize the social welfare (total network throughput). Then we propose a distributed mechanism that can achieve the globally optimal equilibrium. Simulation results verify our proposed approach.