A Game Theoretic Analysis for Energy Efficient Heterogeneous Networks

Smooth and green future extension/scalability (e.g., from sparse to dense, from small-area dense to large-area dense, or from normal-dense to super-dense) is an important issue in heterogeneous networks. In this paper, we study energy efficiency of heterogeneous networks for both sparse and dense two-tier small cell deployments. We formulate the problem as a hierarchical (Stackelberg) game in which the macro cell is the leader whereas the small cell is the follower. Both players want to strategically decide on their power allocation policies in order to maximize the energy efficiency of their registered users. A backward induction method has been used to obtain a closed-form expression of the Stackelberg equilibrium. It is shown that the energy efficiency is maximized when only one sub-band is exploited for the players of the game depending on their fading channel gains. Simulation results are presented to show the effectiveness of the proposed scheme.Comment: 7 pages, 3 figures, in Wiopt 201

Pricing and Resource Allocation via Game Theory for a Small-Cell Video Caching System

Evidence indicates that downloading on-demand videos accounts for a dramatic increase in data traffic over cellular networks. Caching popular videos in the storage of small-cell base stations (SBS), namely, small-cell caching, is an efficient technology for reducing the transmission latency whilst mitigating the redundant transmissions of popular videos over back-haul channels. In this paper, we consider a commercialized small-cell caching system consisting of a network service provider (NSP), several video retailers (VR), and mobile users (MU). The NSP leases its SBSs to the VRs for the purpose of making profits, and the VRs, after storing popular videos in the rented SBSs, can provide faster local video transmissions to the MUs, thereby gaining more profits. We conceive this system within the framework of Stackelberg game by treating the SBSs as a specific type of resources. We first model the MUs and SBSs as two independent Poisson point processes, and develop, via stochastic geometry theory, the probability of the specific event that an MU obtains the video of its choice directly from the memory of an SBS. Then, based on the probability derived, we formulate a Stackelberg game to jointly maximize the average profit of both the NSP and the VRs. Also, we investigate the Stackelberg equilibrium by solving a non-convex optimization problem. With the aid of this game theoretic framework, we shed light on the relationship between four important factors: the optimal pricing of leasing an SBS, the SBSs allocation among the VRs, the storage size of the SBSs, and the popularity distribution of the VRs. Monte-Carlo simulations show that our stochastic geometry-based analytical results closely match the empirical ones. Numerical results are also provided for quantifying the proposed game-theoretic framework by showing its efficiency on pricing and resource allocation.Comment: Accepted to appear in IEEE Journal on Selected Areas in Communications, special issue on Video Distribution over Future Interne

On the Two-user Multi-carrier Joint Channel Selection and Power Control Game

In this paper, we propose a hierarchical game approach to model the energy efficiency maximization problem where transmitters individually choose their channel assignment and power control. We conduct a thorough analysis of the existence, uniqueness and characterization of the Stackelberg equilibrium. Interestingly, we formally show that a spectrum orthogonalization naturally occurs when users decide sequentially about their transmitting carriers and powers, delivering a binary channel assignment. Both analytical and simulation results are provided for assessing and improving the performances in terms of energy efficiency and spectrum utilization between the simultaneous-move game (with synchronous decision makers), the social welfare (in a centralized manner) and the proposed Stackelberg (hierarchical) game. For the first time, we provide tight closed-form bounds on the spectral efficiency of such a model, including correlation across carriers and users. We show that the spectrum orthogonalization capability induced by the proposed hierarchical game model enables the wireless network to achieve the spectral efficiency improvement while still enjoying a high energy efficiency.Comment: 31 pages, 13 figures, accepted in IEEE Transactions on Communication