This paper brings the novel idea of paying the utility to the winning agents in terms of some physical entity in cooperative communications. Our setting is a secret two-way communication channel where two transmitters exchange information in the presence of an eavesdropper. The relays are selected from a set of interested parties such that the secrecy sum rate is maximized. In return, the selected relay nodes' energy harvesting requirements will be fulfilled up to a certain threshold through their own payoff so that they have the natural incentive to be selected and involved in the communication. However, relays may exaggerate their private information in order to improve their chance to be selected. Our objective is to develop a mechanism for relay selection that enforces them to reveal the truth since otherwise they may be penalized. We also propose a joint cooperative relay beamforming and transmit power optimization scheme based on an alternating optimization approach. Note that the problem is highly non-convex since the objective function appears as a product of three correlated Rayleigh quotients. While a common practice in the existing literature is to optimize the relay beamforming vector for given transmit power via rank relaxation, we propose a second-order cone programming (SOCP)-based approach in this paper which requires a significantly lower computational task. The performance of the incentive control mechanism and the optimization algorithm has been evaluated through numerical simulations.