Nash Bargaining Based Economic Analysis of Cognitive Cellular Networks

In this paper, we consider an opportunistic cognitive radio (CR) network comprising of a primary base station (PBS) and a secondary base station (SBS), both associated with multiple users. SBS obtains the right to use the licensed spectrum of PBS by paying a remuneration. Moreover, both PBS and SBS provide service to their corresponding users in exchange of an economic price. PBS, being a profit maximizer, optimally balances between the revenue directly coming from its own users and the monetary reward provided by SBS. On the other hand, SBS must maintain a positive gain to support its infrastructure. Thus, a two-person non-cooperative bargaining game is formulated where both PBS and SBS concur at the values of two parameters, i.e., the activity factor of PBS and the payment made by SBS for opportunistically accessing the licensed spectrum. PBS has knowledge of detection and false-alarm probabilities of the spectrum sensing by SBS and hence can infer how the interference created by missed detection can degrade its achievable capacity. In this framework, we utilize Nash solution to determine a mutually beneficial outcome of the bargaining process. The solution leads to a mathematical relation dictating the viability of the network in the long-run. This result holds for arbitrary continuous user demand functions. For linear user demand, we obtain closed-form expression of the bargaining solution that enables us to analyze the influence of different key system parameters on the economic outcomes.