A game theoretic approach to eavesdropper cooperation in MISO wireless networks

Information theoretic security, also called secrecy analysis, provides theoretical limit for secret data transmission even in wireless networking environment, and it is more focused in these days because of increasing number of private information transmission through wireless channel and its inherent broadcasting characteristic. However, many studies in secrecy analysis assume that there exists only one eavesdropper or there is no cooperation among multiple eavesdroppers, which makes research results difficult to be applied in real situations. In this paper, we conduct a game theoretic analysis of eavesdropper cooperation in MISO wireless communication system where a secret information sender, Alice, has a counter-strategy against eavesdropping. We assume that Alice has a method for preventing eavesdroppers from overhearing. It is triggered by eavesdropper detection and degrades eavesdropping channel by forwarding artificial noise. For this reason, eavesdroppers´ cooperation can pose a high risk to them and we utilize game theory to investigate eavesdropper behavior based on mutual information I (X; Yeve) between the input X from Alice and the output Yeve to an eavesdropper. We derive that non-cooperation is Nash Equilibrium in one shot eavesdropper cooperation game and show necessary conditions for eavesdropper cooperation in infinitely repeated game.