Price of Anarchy for Cognitive MAC Games

In this paper, we model and analyze the interactions between secondary users in a spectrum overlay cognitive system as a cognitive MAC game. In this game, each secondary user can sense (and transmit) one of several channels, the availability of each channel is determined by the activity of the corresponding primary user. We show that this game belongs to the class of congestion game and thus there exists at least one Nash Equilibrium. We focus on analyzing the worst case efficiency loss (i.e., price of anarchy) at any Nash Equilibrium of such a game. Closed-form expressions of price of anarchy are derived for both symmetric and asymmetric games, with arbitrary channel and user heterogeneity. Several insights are also derived in terms of how to design better cognitive radio systems with less severe efficiency loss.