The connectivity of a communication link requires that the signal level be maintained at a threshold level above the noise floor. This is challenging when the link faces adversarial interference. In this paper, the problem of maintaining the link connectivity between a transmitter and receiver facing hostile interference is investigated using a game-theoretical formulation. The strategies for the rivals are the power levels employed by each, yielding a continuum of strategies for each player. Requiring that the signal to interference plus noise (SINR) level is higher than a threshold results in discontinuous player payoffs, and further results in the non-existence of a Nash equilibrium, thereby making the system unstable. However, observing the similarity between this game and the war of attrition game, we extend set of feasible strategies to mixed strategies that belong to the set of all measures over the continuum of feasible power levels. Using this observation, we prove that the equilibrium exists, is unique, and that the extension of the feasible strategies stabilizes the system.