Optimal Pricing Strategy for Operators in Cognitive Femtocell Networks

Cognitive femtocell has been envisioned as a promising technology for covering indoor environment and assisting heavy-loaded macrocell network. Although lots of technical issues of cognitive femtocell network have been studied, e.g., spectrum sharing, interference mitigation, etc., the economic issues that are very important for practical femtocell deployment have not been well investigated in the literatures. In this paper, we focus on the pricing issues in the cognitive femtocell network and propose a two-tier pricing game theoretic framework with two models: static and dynamic pricing models. In the static pricing model, we derive the closed-form expressions for pricing and demand functions, as well as the Nash equilibrium pricing strategies for both macrocell and femtocell operators. In the dynamic pricing model, we first model the cognitive users´ network access behavior as a two-dimensional Markov decision process and propose a modified value iteration algorithm to find the best strategy profiles for cognitive users. Based on the analysis of users´ behavior, we further design an iterative gradient descent algorithm to find the Nash equilibrium pricing strategies for both macrocell and femtocell operators. Simulation results verify our theoretic analysis and show that the proposed algorithm in the dynamic pricing model can quickly converge to the Nash equilibrium prices.