Economic Analysis of Cognitive Underlay Networks: A Nash Bargaining Based Approach

We analyse a cognitive underlay network containing multiple primary and secondary transceivers. The transmitters have access to the instantaneous gains of their associated direct channels but are aware of only the statistical description of other channel gains. Via a Nash bargaining game, they mutually decide their transmission power profiles and the remuneration that the secondary must pay to the primary for utilising the licensed band. We prove that the pairwise feasible utilities of these users form a compact and convex set that ensures the existence and uniqueness of the Nash bargaining solution (NBS). We demonstrate that the computation of the NBS is equivalent to a two-variable functional optimization. We devise an algorithm to tackle this problem and subsequently show its convergence. The numerical results provide several insights about the economics of the network. For example, we explore how different channel distribution parameters impact the sustainability and the economic outcomes of the network.