To ensure security in data transmission is one of the most important issues for wireless relay networks, and physical layer security is an attractive alternative solution to address this issue. In this paper, we consider a cooperative network, consisting of one source node, one destination node, one eavesdropper node, and a number of relay nodes. Specifically, the source may select several relays to help forward the signal to the corresponding destination to achieve the best security performance. However, the relays may have the incentive not to report their true private channel information in order to get more chances to be selected and gain more payoff from the source. We propose a Vickey-Clark-Grove (VCG) based mechanism and an Arrow-d'Aspremont-Gerard-Varet (AGV) based mechanism into the investigated relay network to solve this cheating problem. In these two different mechanisms, we design different "transfer payment" functions to the payoff of each selected relay and prove that each relay gets its maximum (expected) payoff when it truthfully reveals its private channel information to the source. And then, an optimal secrecy rate of the network can be achieved. After discussing and comparing the VCG and AGV mechanisms, we prove that the AGV mechanism can achieve all of the basic qualifications (incentive compatibility, individual rationality and budget balance) for our system. Moreover, we discuss the optimal quantity of relays that the source node should select. Simulation results verify efficiency and fairness of the VCG and AGV mechanisms, and consolidate these conclusions.