text: 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.
  @cite_18: In this work we study joint pricing and power allocation for Dynamic Spectrum Access (DSA) networks with Stackelberg game. In our model, Primary User (PU) is the game leader and jointly determines its power allocation (to guarantee its QoS requirement) and the interference price charged to Secondary User (SU) (to reap revenue). Meanwhile, SU is the game follower and determines its power demand in response to PU's decisions. We quantify PU's and SU's benefit from the channel sharing model by deriving the Stackelberg equilibrium. Our results show that PU's equilibrium profit is asymptotically upper bounded with its marginal power cost and rate requirement. A distributed algorithm is proposed to find the equilibrium. We also propose an incentive-compatible mechanism for PU and SU to keep the social welfare optimum cooperatively. We extend our Stackelberg game to the multiple SUs scenario, where the interference among SUs results in a noncooperative power demand subgame. We propose a low-complexity heuristic algorithm for PU to maximize its profit. Our results show that PU can benefit by selecting multiple SUs to share its channel if SUs' mutual interference is limited.
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  @cite_8: 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.
  @cite_5: Market-based mechanisms offer promising approaches for spectrum access in cognitive radio networks. In this paper, we focus on two market models, one with a monopoly primary user (PU) market and the other with a multiple PU market, where each PU sells its temporarily unused spectrum to secondary users (SUs). We propose a pricing-based spectrum trading mechanism that enables SUs to contend for channel usage by random access, in a distributed manner, which naturally mitigates the complexity and time overhead associated with centralized scheduling. For the monopoly PU market model, we first consider SUs contending via slotted Aloha. The revenue maximization problems here are nonconvex. We first characterize the Pareto optimal region, and then obtain a Pareto optimal solution that maximizes the SUs' throughput subject to the SUs' budget constraints. To mitigate the spectrum underutilization due to the “price of contention,” we revisit the problem where SUs contend via CSMA, and show that spectrum utilization is enhanced, resulting in higher revenue. When the PU's unused spectrum is a control parameter, we study further the tradeoff between the PU's utility and its revenue. For the multiple PU market model, we cast the competition among PUs as a three-stage Stackelberg game, where each SU selects a PU's channel to maximize its throughput. We characterize the Nash equilibria, in terms of access prices and the spectrum offered to SUs. Our findings reveal that the number of equilibria exhibits a phase transition phenomenon, in the sense that when the number of PUs is greater than a threshold, there exist infinitely many equilibria; otherwise, there exists a unique Nash equilibrium, where the access prices and spectrum opportunities are determined by the budgets elasticity of SUs and the utility level of PUs.
  @cite_17: With the development of cognitive radio technologies, dynamic spectrum access becomes a promising approach to increase the efficiency of spectrum utilization and solve spectrum scarcity problem. Under dynamic spectrum access, unlicensed wireless users (secondary users) can dynamically access the licensed bands from legacy spectrum holders (primary users) on an opportunistic basis. While most primary users in existing works assume secondary transmissions as negative interference and don't actively involve them into the primary transmission, in this paper, motivated by the idea of cooperative communication, we propose a cooperative cognitive radio framework, where primary users, aware of the existence of secondary users, may select some of them to be the cooperative relay, and in return lease portion of the channel access time to them for their own data transmission. Secondary users cooperating with primary transmissions have the right to decide their payment made for primary user in order to achieve a proportional access time to the wireless media. Both primary and secondary users target at maximizing their utilities in terms of their transmission rate and revenue payment. This model is formulated as a Stackelberg game and a unique Nash Equilibrium point is achieved in analytical format. Based on the analysis we discuss the condition under which cooperation will increase the performance of the whole system. Both analytical result and numerical result show that the cooperative cognitive radio framework is a promising framework under which the utility of both primary and secondary system are maximized.
summary: 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.