Optimal power allocation over parallel Gaussian channels in cognitive radio and jammer games

Cognitive jammers are able to deploy advanced strategies that degrade the performance of cognitive radio user communications. In this paper, we study the problem of power allocation in cognitive radio user and jammer games, over parallel Gaussian channels. We model the interaction between a communicator (a transmitter-receiver pair) and a jammer using zero-sum games with continuous action sets; we describe unilateral, Nash and stackelberg games. We compare the Nash equilibrium, the Stackelberg equilibrium and the minmax/maxmin optimal power allocations through the simulation of the diverse game scenarios. Finally, we give the theoretical proof of existence and uniqueness of the Nash equilibrium.