A Multi-Jammer Power Control Game

We consider a single carrier communication system subjected to multi-jammer interference, and study optimal power control in the framework of game theory. The Nash and Stackelberg equilibria are derived in closed form. Conditions involving the background noise variance and the transmission cost are established for determining whether the equilibria are unique. It is proven that in the case of multiple equilibria, the user has the same payoff at each equilibrium, which reflects the stability of the communication. Also, consistent with the literature on single-jammer scenarios, it is shown that when the jammers are in a Stackelberg game, although they act as followers, they gain in payoffs as compared to the Nash game.