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Resource allocation is considered for cooperative transmissions in multiple-relay wireless networks. Two auction mechanisms, SNR auctions and power auctions, are proposed to distributively coordinate the allocation of power among multiple relays. In the SNR auction, a user chooses the relay with the lowest weighted price. In the power auction, a user may choose to use multiple relays simultaneously, depending on the network topology and the relays' prices. Sufficient conditions for the existence (in both auctions) and uniqueness (in the SNR auction) of the Nash equilibrium are given. The fairness of the SNR auction and efficiency of the power auction are further discussed. It is also proven that users can achieve the unique Nash equilibrium distributively via best response updates in a completely asynchronous manner.