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The authors consider a cognitive radio network in which multiple pairs of Secondary Users (SUs) communicate by a one-way relay node over orthogonal channels with the existence of an eavesdropper close to the destination. The transmit power of the relay needs efficient distribution for maximizing the sum secrecy rate of the SU pairs, meanwhile satisfying the interference constraint at the single Primary User (PU). Specifically, they introduce two multi-object auctions, i.e., the Vickrey auction and the sequential first-price auction, to perform this power allocation problem. They prove the existence and give the general form of the only equilibrium for each auction.
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