Request Delay-Based Pricing for Proactive Caching: A Stackelberg Game Approach

Proactively pushing content to users has emerged as a promising approach to improve the spectrum usage in off-peak times for fifth-generation mobile networks. However, owing to the uncertainty of future user demands, base stations (BSs) may not receive payments for the pushed files. To motivate content pushing, providing economic incentives to BSs becomes essential. Based on request delay information (RDI) that characterizes the users' request time for content files, this paper studies the profit maximization for a BS and a spectrum provider (SP) by developing a Stackelberg game. Specifically, the SP sets different selling prices of bandwidth for pushing and on-demand services, while the BS responds with the optimal quantity to purchase. In the game with non-causal RDI, a sub-gradient algorithm is presented to achieve a Stackelberg equilibrium (SE). For the game with statistical RDI, a closed-form expression is derived for an SE in the single-user scenario and a simulated annealing-based algorithm is designed to obtain an SE in the multi-user scenario. It is shown that the proposed games achieve greater profit for both the SP and the BS, compared with the on-demand scheme. Furthermore, pricing with statistical RDI attains performance closely approaching that with non-causal RDI, while being more practical.