A Jamming Game With Rival-Type Uncertainty

We consider the communication between a source (user) and a destination in the presence of a jammer, and study resource assignment in a non-cooperative game theory framework. A player (the user or the jammer) has incomplete information about its rival's identity in the form of uncertainty; the player only knows the probabilities that its rival is a player implementing a behavioral strategy as a follower in a Stackelberg game (smart-type), or selects a feasible strategy as in a Nash game (regular-type). We model the problem as two Bayesian games. In the first game, the user has incomplete information about the jammer, and in the second game, the jammer has incomplete information about the user. The user's utility is throughput. We prove that a unique equilibrium exists and derive it in closed form as a function of the known probabilities. We show that the Nash and Stackelberg equilibria are boundary cases of the obtained equilibrium. Thus, our approach allows one to incorporate the Nash and Stackelberg equilibria into a unified scale of equilibria. Monotonicity properties of the equilibrium strategies and the corresponding payoffs with respect to the network parameters are proven, and also supported by simulations.