A FrequencyHopping Game Between a Smart Jammer and a Cognitive Radio A smart jammer can determine the frequencyhopping patterns of a cognitive radio using machine learning. This paper develops a twostate stochastic game where the receiver and jammer choose at each stage whether to stay on their current frequency or hop to a new one. The cost of hopping to a new frequency is also modeled with a discounted payoff. Machine learning algorithms are implemented to update the policies for both players in order to converge to a stationary Nash equilibrium. The game is simulated using Nash Qlearning and WoLF PHC, as well as the computed singlestage Nash equilibrium for each state. Of the strategy options included for both players, there are ideal strategyupdating algorithm pairs depending on the values used for the discounted payoffs.

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 userxe2x80x99s transmission utility is the signaltointerference 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 smarttype 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 tradeoff between smartjamming and regularjamming attacks.