Pricing, Spectrum Sharing, and Service Selection in Two-Tier Small Cell Networks: A Hierarchical Dynamic Game Approach

Abstract

Small cells overlaid with macrocells can increase the capacity of two-tier cellular wireless networks by offloading traffic from macrocells. To motivate the small cell service providers (SSPs) to open portion of the access opportunities to macro users (i.e., to operate in a hybrid access mode), we design an incentive mechanism in which the macrocell service provider (MSP) could pay to the SSPs. According to the price offered by the MSP, the SSPs decide on the open access ratio, which is the ratio of shared radio resource for macro users and the total amount of radio resource in a small cell. The users in this two-tier network can make service selection decisions dynamically according to the performance satisfaction level and cost, which again depend on the pricing and spectrum sharing between the MSP and SSPs. To model this dynamic interactive decision problem, we propose a hierarchical dynamic game framework. In the lower level, we formulate an evolutionary game to model and analyze the adaptive service selection of users. An evolutionary stable strategy (ESS) is considered to be the solution of this game. In the upper level, the MSP and SSPs sequentially determine the pricing strategy and the open access ratio, respectively, taking into account the distribution of dynamic service selection at the lower-level evolutionary game. A Stackelberg differential game is formulated where the MSP and SSPs act as the leader and followers, respectively. An open-loop Stackelberg equilibrium is considered to be the solution of this game. We also extend the hierarchical dynamic game framework and investigate the impact of information delays on the equilibrium solutions. Numerical results show the effectiveness and advantages of dynamic control of the open access ratio and pricing.