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 sumrate 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.