  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.
