A Power Control Game with Uncertainty On the Type of the Jammer

We consider a single carrier communication system subjected to jamming, and study optimal power control in the framework of game theory. The user's transmission utility is the signal-to-interference plus noise ratio (SINR), and the user does not know with certainty whether the jammer is smart (i.e., it follows the best response strategy according to a Stackelberg game) or regular (i.e., it maximizes its payoff independent of the user, according to a Nash game). We formulate the problem as a Bayesian game, where the user knows only the probability of each jammer type (smart or regular), and find the equilibrium strategies in closed form. We show that the more probable a smart-type jammer is, the higher the payoffs of both players are. Considering the probability of each jammer type as a control parameter, and based on proportional fairness criteria, we find the optimal trade-off between smart-jamming and regular-jamming attacks.