Antieavesdropping with Selfish Jamming in Wireless Networks: A Bertrand Game Approach

Wireless communications are vulnerable to eavesdropping attacks due to their broadcast nature. To deal with their emerging challenge of physical layer security, in this paper, we study the antieavesdropping problem in the presence of selfish jammers, who desire to achieve maximum profit for themselves. We consider both the single-channel multijammer (SCMJ) model and the multichannel single-jammer (MCSJ) model. We investigate the interaction between the source that transmits secret information and friendly jammer nodes who assist the source by interfering with the eavesdropper. This problem is formulated as an oligopoly market consisting of a few firms and a buyer. By modeling the problem as a Bertrand game based on price competition, we obtain the optimal pricing scheme for the friendly, while for selfish jammers, the utility of those jammers is maximized. For the SCMJ model, we prove the existence of Bertrand Equilibrium by deriving a closed-form expression for the optimal price strategy. For the MCSJ model, a closed-form expression for power allocation is derived, based on which a new algorithm is designed to obtain the optimal strategy of the jammer. Finally, via simulations, we verify our theoretical analysis.