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Power allocation using Vickrey auction and sequential first-price auction games for physical layer security in cognitive relay networks

We 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, we introduce two multi-object auctions, i.e. the Vickrey auction and the sequential first-price auction, to perform this power allocation problem. We prove the existence and give the general form of the only equilibrium for each auction. We also propose two algorithms based on the equilibriums, respectively. From the simulation results, we see that the system secrecy rate curve of the Vickrey auction gradually coincides with that of the optimal allocation with increasing power units, while the sequential first-price auction reflects more fairness.