Hierarchical Market Competition in a Duopoly Super Wi-Fi Spectrum Market

Super Wi-Fi refers to Wi-Fi-like Internet access via spectrum white spaces (WS), which is expected to enhance today's Wi-Fi thanks to the superior propagation characteristics of the WS compared to ISM/UNII bands. A Super Wi-Fi wireless service provider (WSP) dynamically leases and opportunistically utilizes a licensed band while it is temporarily unoccupied by its (licensed) primary users (PUs). The PUs' spectrum usage pattern presents time-varying spectrum availability, thus necessitating eviction of in-service customers upon return of PUs where the evicted customers are compensated with partial reimbursement of their service charge. This paper investigates the dynamics of a duopoly Super Wi-Fi market where two co-located WSPs compete for leasing better quality channels and for setting competitive service price to entice more customers. The channel quality is measured by the PUs' utilization factor (smaller the better). Since higher quality channels possess more WS incurring larger channel leasing cost, a WSP should strike a balance between channel quality and service tariff in maximizing its profit. The market competition is modeled as hierarchical noncooperative price- and quality-games, and their Nash Equilibria (NE) are derived. In addition, we investigate the impact of differentiated reimbursement rates and limited channel availability. Finally, we demonstrate the tradeoffs among leasing cost, customer arrival rate, and channel characteristics via numerical analyses.