Multiple Access Game with a Cognitive Jammer

We consider a two-user multiple access game in which one player (primary user) is interested in maximizing its data rate at the minimum possible transmission power and the other player (secondary, cognitive user) can either jam the primary traffic or coordinate with the primary user and send its own message to the common destination. The cognitive user employs noise forwarding as a leverage to maximize its own data rate by forcing the primary user to decrease its power level. First, the unique Nash equilibrium of the non-cooperative static game is derived and shown to be in efficient for certain ranges of channel gains and cost parameters. Then, a Stackelberg game formulation is considered in which the primary user is the leader. Here, interestingly, it is shown that the secondary accepts to play as the follower where the Stackelberg equilibrium dominates the Nash equilibrium and hence lose-lose situations are eliminated.