A Fair Anti-Eavesdropping Strategy for Communication with Several Receivers

Wireless network communication of a transmitter with a group of receivers (nodes) is susceptible to malicious eavesdropping attacks. In this paper, motivated by the observation that maximizing the secrecy rate protocol might lead to neglecting communication with some nodes, we suggest designing a protocol to maximize fairness of the secrecy rates, specifically, α− fairness, in the transmitter's communication with all the nodes. The problem is modeled in a non-zero-sum game-theoretical framework between a transmitter and an adversary (eavesdropper). Equilibrium strategies are derived in closed form and their uniqueness is proven which reflects the stability of the suggested transmission protocol. Moreover, although an equilibrium is established as unique for each fixed fairness coefficient, all together it results in a continuum of transmission protocols, one protocol per fairness coefficient. To deal with this issue, in this paper, we suggest using a trade-off fairness coefficient between the expected secrecy rate of the whole nodes' group and the expected secrecy rate of the worst-off secrecy rate node, reflecting "a weak link" in the communication, as the best protocol among all such fair protocols in its application. The derived equilibria and trade-off fairness coefficient are numerically illustrated.