Monotone games for cognitive radio systems

Noncooperative game theory is a branch of game theory for the resolution of conflicts among interacting decision makers (called players), each behaving selfishly to optimize his own well-being. In this chapter, we present a mathematical treatment of (generalized) Nash equilibrium problems based on the variational inequality and complementarity approach, covering the topics of existence and uniqueness of an equilibrium, and the design of distributed algorithms using best-response iterations along with their convergence properties.We then apply the developed machinery to the distributed design of cognitive radio systems. The proposed equilibrium models and resulting algorithms differ in performance of the secondary users, level of protection of the primary users, computational effort and signaling among primary and secondary users, convergence analysis, and convergence speed; which makes them suitable for many different CR systems.