Max-Min Strategies for Power-Limited Games in the Presence of Correlated Jamming

In tactical (or commercial) wireless communication systems, a jammer (or hacker) may be present to disrupt the link of legitimate users with an access point (AP). In this context, we introduce a game-theoretic max-min formulation for multiple access in the presence of the correlated jamming, replacing the mutual information game setup that has been studied so far. The novel formulation is well-suited for power-limited systems. Specifically, the AP strives to maximize the network´s lifetime by minimizing sum-power while guaranteeing a minimum sum-rate for the users. We show that the AP´s optimal strategy is a greedy one which allocates power to the strongest user, while the jammer´s best response is to reduce the aggregate channel gain of the strongest user as much as possible. Hence, the multiuser game with a sum-rate constraint is equivalent to a single-user game where only the strongest user is present. Numerical results verify the correlated jammer´s improved capability to inflict severe disruption in low data rate and low user channel gain settings. However, in a high data rate regime, generating white noise is the jammer´s best strategy.