In this paper, we investigate a wireless-powered relays assisted batteryless IoT network based on the non-linear energy harvesting model, where there exists an energy service provider constituted by the hybrid access point (HAP) and an IoT service provider constituted by multiple clusters. The HAP provides energy signals to the batteryless devices for information backscattering and the wireless-powered relays for energy harvesting. The relays are deployed to assist the batteryless devices with the information transmission to the HAP by using the harvested energy. To model the energy interactions between the energy service provider and IoT service provider, we propose a Stackelberg game based framework. We aim to maximize the respective utility values of the two providers. Since the utility maximization problem of the IoT service provider is non-convex, we employ the fractional programming theory and propose a block coordinate descent (BCD) based algorithm with successive convex approximation (SCA) and semi-definite relaxation (SDR) techniques to solve it. Numerical simulation results confirm that compared to the benchmark schemes, our proposed scheme can achieve larger utility values for both the energy service provider and IoT service provider.

With the popularity of smart devices, mobile crowdsensing, in which the crowdsensing platform gathers useful data from users of smart devices, e.g., smartphones, has become a prevalent paradigm. Various incentive mechanisms have been extensively adopted for the crowdsensing platform to incentivize users of smart devices to offer sensing data. Existing works have concentrated on rewarding smart-device users for their short term effort to provide data without considering the long-term factors of smart-device users and the quality of data. Our previous work has considered the quality of data of smart-device users by incorporating the long-term reputation of smart-device users. However, our previous work only considered a quality maximization problem with budget constraints on one location. In this paper, multiple locations are considered. Stackelberg game is utilized to solve a two-stage optimization problem. In the first stage, the crowdsensing platform allocates the budget to different locations and sets price as incentives for users to maximize the total data quality. In the second stage, the users make efforts to provide data to maximize its utility. Extensive numerical simulations are conducted to evaluate proposed algorithm.

In this letter, we study an interference scenario under a smart interferer which observes color channels and interferes with a visible light communication (VLC) network. We formulate the smart interference problem based on a Stackelberg game and propose an optimal response algorithm to overcome the interference by optimizing transmit power and sub-color channel allocation. The proposed optimization algorithm is composed with Lagrangian dual decomposition and non-linear fractional programming to have stability to get optimum points. Numerical results show that the utility by the proposed algorithm is increased over that of the algorithm based on the Nash game and the baseline schemes.

To tackle the distributed power optimization problems in wireless sensor networks localization systems, we model the problem as a hierarchical game, i.e. a multi-leader multi-follower Stackelberg game. Existing researches focus on the power allocation of anchor nodes for ranging signals or the power management of agent nodes for cooperative localization, individually. However, the power optimizations for different nodes are indiscerptible due to the common objective of localization accuracy. So it is a new challenging task when the power allocation strategies are considered for anchor and agent nodes simultaneously. To cope with this problem, a hierarchical game is proposed where anchor nodes are modeled as leaders and agent nodes are modeled as followers. Then, we prove that games of leaders and followers are both potential games, which guarantees the Nash equilibrium (NE) of each game. Moreover, the existence of Stackelberg equilibrium (SE) is proved and achieved by the best response dynamics. Simulation results demonstrate that the proposed algorithm can have better localization accuracy compared with the decomposed algorithm and uniform strategy.

This paper investigates the spectrum allocation problem. Under the current spectrum management mode, large amount of spectrum resource is wasted due to uncertainty of user's demand. To reduce the impact of uncertainty, a presale mechanism is designed based on spectrum pool. In this mechanism, the spectrum manager provides spectrum resource at a favorable price for presale aiming at sharing with user the risk caused by uncertainty of demand. Because of the hierarchical characteristic, we build a spectrum market Stackelberg game, in which the manager acts as leader and user as follower. Then proof of the uniqueness and optimality of Stackelberg Equilibrium is given. Simulation results show the presale mechanism can promote profits for both sides and reduce temporary scheduling.

In this letter, we investigate the price-based power allocation for non-orthogonal multiple access (NOMA) networks, where the base station (BS) can admit the users to transmit by pricing their power. Stackelberg game is utilized to model the pricing and power purchasing strategies between the BS and the users. Based on backward induction, the pricing problem of the BS is recast into the non-convex power allocation problem, which is equivalent to the rate allocation problem by variable replacement. Based on the equivalence problem, an optimal price-based power allocation algorithm is proposed to maximize the revenue of the BS. Simulation results show that the proposed algorithm is superior to the existing pricing algorithm in items of the revenue of BS and the number of admitted users.

Price-based power control problem is investigated in the spectrum sharing cognitive radio networks (CRNs) by Stackelberg game. Using backward induction, the revenue function of the primary user (PU) is expressed as a non-convex function of the transmit power of the secondary users (SUs). To solve the non-convex problem of the PU, a branch and bound based price-based power control algorithm is proposed. The proposed algorithm can be used to provide performance benchmarks for any other low complexity sub-optimal price-based power control algorithms based on Stackelberg game in CRNs.

In this letter, we investigate the price-based power allocation with rate proportional fairness constraint in downlink non-orthogonal multiple access (NOMA) systems. The Stackelberg game is utilized to model the interaction between the base station (BS) and users. The revenue maximization problem of the BS is first converted to rate allocation problem, then the optimal rate allocation for each user is obtained by variable substitution. Finally, a price-based power allocation with rate proportional fairness (PAPF) algorithm is proposed based on the relationship between rate and transmit power. Simulation results show that the proposed PAPF algorithm is superior to the previous price-based power allocation algorithm in terms of fairness index and minimum normalized user (MNU) rate.

This letter studies the price-based power control algorithm for the spectrum sharing cognitive radio networks. The primary user (PU) profits from the secondary users (SUs) by pricing the interference power made by them. The SUs cooperate with each other to maximize their sum revenue with the signal-to-interference plus noise ratio (SINR) balancing condition. The interaction between the PU and the SUs is modeled as a Stackelberg game. Closed-form expressions of the optimal price for the PU and power allocation for the SUs are given. Simulation results show the proposed algorithm improves the revenue of both the PU and fairness of the SUs compared with the uniform pricing algorithm.

This paper investigates open-loop Stackelberg games for a class of stochastic systems with multiple players. First, the necessary conditions for the existence of an open-loop Stackelberg strategy set are established using the stochastic maximum principle. Such conditions can be represented as solvability conditions for cross-coupled forward-backward stochastic differential equations (CFBSDEs). Second, in order to obtain the open-loop strategy set, a computational algorithm based on a four-step scheme is developed. A numerical example is then demonstrated to show the validity of the proposed method.

Spectrum sharing effectively improves the spectrum usage by allowing secondary users (SUs) to dynamically and opportunistically share the licensed bands with primary users (PUs). The concept of cooperative spectrum sharing allows SUs to use portions of the PUs' radio resource for their own data transmission, under the condition that SUs help the PUs' transmission. The key issue with designing such a scheme is how to deal with the resource splitting of the network. In this paper we propose a relay-based cooperative spectrum sharing scheme in which the network consists of one PU and multiple SUs. The PU asks the SUs to relay its data in order to improve its energy efficiency, in return it rewards the SUs with a portion of its authorized spectrum. However each SU is only allowed to transmit its data via the rewarded channel at a power level proportional to the contribution it makes to the PU. Since energy cost is considered, the SUs must carefully determine their power level. This scheme forms a non-cooperative Stackelberg resource allocation game where the strategy of PU is the bandwidth it rewards and the strategy of each SU is power level of relay transmission. We first investigate the second stage of the sub-game which is addressed as power allocation game. We prove there exists an equilibrium in the power allocation game and provide a sufficient condition for the uniqueness of the equilibrium. We further prove a unique Stackelberg equilibrium exists in the resource allocation game. Distributed algorithms are proposed to help the users with incomplete information achieve the equilibrium point. Simulation results validate our analysis and show that our proposed scheme introduces significant utility improvement for both PU and SUs.

In this paper, an infinite-horizon team-optimal incentive Stackelberg strategy is investigated for a class of stochastic linear systems with many non-cooperative leaders and one follower. An incentive structure is adopted which allows for the leader's team-optimal Nash solution. It is shown that the incentive strategy set can be obtained by solving the cross-coupled stochastic algebraic Riccati equations (CCSAREs). In order to demonstrate the effectiveness of the proposed strategy, a numerical example is solved.

This paper studies the impact of integrating pricing with connection admission control (CAC) on the congestion management practices in contention-based wireless random access networks. Notably, when the network is free of charge, each self-interested user tries to occupy the channel as much as possible, resulting in the inefficient utilization of network resources. Pricing is therefore adopted as incentive mechanism to encourage users to choose their access probabilities considering the real-time network congestion level. A Stackelberg leader-follower game is formulated to analyze the competitive interaction between the service provider and the users. In particular, each user chooses the access probability that optimizes its payoff, while the self-interested service provider decides whether to admit or to reject the user's connection request in order to optimize its revenue. The stability of the Stackelberg leader-follower game in terms of convergence to the Nash equilibrium is established. The proposed CAC scheme is completely distributed and can be implemented by individual access points using only local information. Compared to the existing schemes, the proposed scheme achieves higher revenue gain, higher user payoff, and higher QoS performance.

A price-based spectrum investment and pricing scheme in cooperative cognitive radio networks is presented to use wireless resource more efficiently in technical and economic aspects. We analyze the impact of cooperative communications and the relationship between spectrum hole cost and leasing cost in the optimal decision of SAP.