This paper investigates the energy-efficient power allocation for a two-tier, underlaid femtocell network. The behaviors of the Macrocell Base Station (MBS) and the Femtocell Users (FUs) are modeled hierarchically as a Stackelberg game. The MBS guarantees its own QoS requirement by charging the FUs individually according to the cross-tier interference, and the FUs responds by controlling the local transmit power non-cooperatively. Due to the limit of information exchange in intra- and inter-tiers, a self-learning based strategy-updating mechanism is proposed for each user to learn the equilibrium strategies. In the same Stackelberg-game framework, two different scenarios based on the continuous and discrete power profiles for the FUs are studied, respectively. The self-learning schemes in the two scenarios are designed based on the local best response. By studying the properties of the proposed game in the two situations, the convergence property of the learning schemes is provided. The simulation results are provided to support the theoretical finding in different situations of the proposed game, and the efficiency of the learning schemes is validated.
When it comes to the resource allocation in hierarchical networks, such as the femtocell networks and cognitive radio networks, the Stackelberg game @cite_7 based modeling is widely preferred since it is able to reflect the features of hierarchy and ad-hoc topology in the network @cite_17 @cite_4 . the Stackelberg game is characterized by the sequential decision making manner (namely, the follower-leader strategy updating), and hence suitable for modeling the heterogeneous user behaviors in the network. Due to the computational intensity for obtaining the Stackelberg Equilibrium (SE), most of the existing studies @cite_8 @cite_18 @cite_5 adopt a utility model that favors the derivation of a closed-form SE, and solve for the SEs through transforming the games as hierarchical optimization problems.
@cite_18 @cite_4 @cite_7 @cite_8 @cite_5 @cite_17
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In this paper, we raise the question: What is the value that demand response management (DRM) can bring to generation companies and consumers in the smart grid? The question is fundamental for understanding the efficiency and impact of DRM on the future power grid. To answer this question, we first establish a Stackelberg game framework that captures the hierarchical communication architecture of the energy system, and the rational behaviors of the consumers and the market operator. We define the value of demand response based on the Stackelberg equilibrium (SE) solution to the hierarchical two-person game problem, and the standard optimal solution to economic dispatch problem. In order to compute the equilibrium solution, we show that a consistency principle can be used to characterize the SE of the game in which the follower responds to the dual variable of the leader's problem. We use logarithmic utility functions to illustrate the solution concept and show that in some cases, DRM provides conflicting values to the gencos and consumers. 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 (SBSs), namely, small-cell caching, is an efficient technology for mitigating redundant data transmissions over backhaul channels in heterogeneous networks (HetNets). In this paper, we consider a commercialized small-cell caching system consisting of a video retailer (VR), multiple network service providers (NSPs), and mobile users (MUs). The VR leases its popular videos to the NSPs to make profits, and the NSPs, after placing these videos to their SBSs, can efficiently reduce the repetitive video transmissions over their backhaul channels. We study such a system within the framework of the Stackelberg game. We first model the MUs and SBSs as two independent Poisson point processes (PPPs) and develop the probability of the event that an MU can obtain the demanded video directly from the memory of an SBS. Then, based on the derived probability, we formulate a Stackelberg game to maximize jointly the average profit of the VR and the NSPs. Moreover, we investigate the Stackelberg equilibrium (SE) via solving an optimization problem. Numerical results are provided for verifying the proposed framework by showing its effectiveness on pricing and resource allocation. This paper introduces a particular game formulation and its corresponding notion of equilibrium, namely the satisfaction form (SF) and the satisfaction equilibrium (SE). A game in SF models the case where players are uniquely interested in the satisfaction of some individual performance constraints, instead of individual performance optimization. Under this formulation, the notion of equilibrium corresponds to the situation where all players can simultaneously satisfy their individual constraints. The notion of SE, models the problem of QoS provisioning in decentralized self-configuring networks. Here, radio devices are satisfied if they are able to provide the requested QoS. Within this framework, the concept of SE is formalized for both pure and mixed strategies considering finite sets of players and actions. In both cases, sufficient conditions for the existence and uniqueness of the SE are presented. When multiple SE exist, we introduce the idea of effort or cost of satisfaction and we propose a refinement of the SE, namely the efficient SE (ESE). At the ESE, all players adopt the action which requires the lowest effort for satisfaction. A learning method that allows radio devices to achieve a SE in pure strategies in finite time and requiring only one-bit feedback is also presented. Finally, a power control game in the interference channel is used to highlight the advantages of modeling QoS problems following the notion of SE rather than other equilibrium concepts, e.g., generalized Nash equilibrium. 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 e This paper investigates price-based resource allocation strategies for two-tier femtocell networks, in which a central macrocell is underlaid with distributed femtocells, all operating over the same frequency band. Assuming that the macrocell base station (MBS) protects itself by pricing the interference from femtocell users, a Stackelberg game is formulated to study the joint utility maximization of the macrocell and femtocells subject to a maximum tolerable interference power constraint at the MBS. Two practical femtocell network models are investigated: sparsely deployed scenario for rural areas and densely deployed scenario for urban areas. For each scenario, two pricing schemes: uniform pricing and non-uniform pricing, are proposed. The Stackelberg equilibriums for the proposed games are characterized, and an effective distributed interference price bargaining algorithm with guaranteed convergence is proposed for the uniform-pricing case. Numerical examples are presented to verify the proposed studies. It is shown that the proposed schemes are effective in resource allocation and macrocell protection for both the uplink and downlink transmissions in spectrum-sharing femtocell networks. This paper proposes a Stackelberg game approach to deal with demand response (DR) scheduling under load uncertainty based on real-time pricing (RTP) in a residential setup. We formulate the optimization problems for the service provider that acts as the leader and for the users who are the multiple followers, respectively. We derive the Stackelberg Equilibrium (SE) consisting of the optimal real-time electricity price and each user's optimal power consumption. Simulation results show the proposed DR scheduling not only can control the total power consumption, but also is beneficial to the service provider's revenue. Moreover, the load uncertainty increases the service provider's revenue and decreases each user's payoff.