Stackelberg Game Framework Research Articles

Call Admission Control With Inter-Network Cooperation for Cognitive Heterogeneous Networks

In this paper, a call admission control algorithm based on inter-network cooperation is proposed via a Stackelberg game framework for cognitive heterogeneous networks. The call admission control problem is subject to the variable bandwidth rate traffic, network service selection, feasible subchannel allocation, and call blocking probability. The call admission control algorithm is based on spectrum price at primary heterogeneous networks and subchannel allocation price and network selection at cognitive heterogeneous networks. In order to determine the call blocking probability, a probability upper bound of exceeding the maximum admission number for secondary mobile terminals (MTs) is analyzed based on ${\mathrm{M}}/{\mathrm{M}}/\infty $ model. Then, the subchannel allocation price and network selection are designed via the dual decomposition method, and the vacant spectrum price is determined with Bertrand game theory. Finally, a call admission control algorithm is proposed. Simulation results demonstrate that the proposed algorithm not only improves quality of service at each secondary MT, but also reduces the call blocking probability for cognitive heterogeneous networks.

Bundle-Pricing Decision Model for Multiple Products

Bundling is an efficient method to achieve business objectives in many industries. However decisions of bundle selection and pricing are complicated when multiple products are involved. In this paper, we investigate a bundle-pricing decision model for multiple products. With the objective to maximize the retailer’s profit, an integrated bundle-pricing model for multiple commodities is formulated as a Non-Linear Mixed Integer Program based on the framework of Stackelberg game. By adding auxiliary decision variables, this model is converted into a Mixed Integer Linear Program and solved by Cplex. Numerical experiments and sensitive analysis are conducted to provide managerial insights for bundling multiple products. It indicates that low consumption level consumers prefer bundles composed of more commodities with lower prices. The products with higher cost level should be bundled with smaller bundle size and higher prices.

Power-Efficient Secure Transmission Against Full-Duplex Active Eavesdropper: A Game-Theoretic Framework

Information security is of paramount importance yet significant challenge for wireless communications. In this paper, we investigate the power-efficient transmissions with security concerns in the presence of a full-duplex (FD) active eavesdropper. With FD capability, the eavesdropper can launch jamming attacks while eavesdropping, which affects the legitimate transmissions, such that the legitimate power allocation becomes more favorable for eavesdropping. However, the jamming attacks require additional power consumption and result in self-interference at the eavesdropper itself. The legitimate user intends for a power-efficient manner to effectively guarantee the secure transmissions to defend against the simultaneous eavesdropping and jamming attacks. We formulate the problem within a Stackelberg game framework, where the eavesdropper takes action first as the leader and the legitimate user acts as the follower. We analyze the security game model for both single-channel and multi-channel cases. Furthermore, by exploring the properties of the game equilibrium, we propose the optimal transmission strategy and jamming strategy for the legitimate transmission and eavesdropping, respectively. Finally, we provide extensive simulation results to corroborate our theoretical analysis and evaluate the security performance.

Auction–Stackelberg game framework for access permission in femtocell networks with multiple network operators

With the explosive growth of indoor data traffic in forthcoming fifth generation cellular networks, it is imperative for mobile network operators to improve network coverage and capacity. Femtocells are widely recognized as a promising technology to address these demands. As femtocells are sold or loaned by a mobile network operator (MNO) to its residential or enterprise customers, MNOs usually employ refunding scheme to compensate the femtocell holders (FHs) providing indoor access to other subscribers by configuring the femtocell to operate in open or hybrid access mode. Due to the selfishness nature, competition between network operators as well as femtocell holders makes it challenging for operators to select appropriate FHs for trading access resources. This inspires us to develop an effective refunding framework, with aim to improve overall network resource utilization, through promoting FHs to make reasonable access permission for well-matched macro users. In this paper, we develop a two-stage auction–Stackelberg game (ASGF) framework for access permission in femtocell networks, where MNO and mobile virtual network operator lease access resources from multiple FHs. We first design an auction mechanism to determine the winner femtocell that fulfils the access request of macro users. We next formulate the access permission problem between the winner femtocell and operators as a Stackelberg game, and theoretically prove the existence of unique equilibrium. As a higher system payoff can be gained by improving individual players’ payoff in the game, each player can choose the best response to others’ action by implementing access permission, while avoiding solving a complicated optimization problem. Numerical results validate the effectiveness of our proposed ASGF based refunding framework and the overall network efficiency can be improved significantly.

Dormancy Mechanism Based Power Allocation in Heterogeneous Networks: A Stackelberg Game Approach

In two-tier heterogeneous networks (HetNets) that consist of a central macrocell underlaid with spectrum-sharing dense smallcells, one primary concern is the cross-tier interference limits the network capacity. On the other hand, dormancy mechanism of smallcells is an emerging technique that can improve energy efficiency and mitigate interference. Therefore in this paper, we propose a power optimization oriented Stackelberg game considering dormancy mechanism for the downlink of two-tier HetNets. First, the smallcell dormancy mechanism is introduced to control the smallcells’ operation. Then the Stackelberg game framework is developed. A sub game based on a potential theory is further formulated to optimize the transmit power of the active smallcells, which is demonstrated to converge to a pure and unique Nash equilibrium. In this sub game, the interference pricing mechanism is employed to price the cross-tier interference caused by smallcells and hence restricts the utility function of smallcells. Simulation results show that the proposed Stackelberg game based on dormancy mechanism with interference pricing can improve the smallcell network throughput and meanwhile reduce the average transmit power of smallcells.

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.

Distributed Interference-Aware Cooperative MAC Based on Stackelberg Pricing Game

Cooperative communication can significantly enhance the efficient utilization of spectrum in wireless networks. The performance of wireless cooperative networks depends on careful medium access control (MAC) and resource allocation such as relay selection and cooperative link scheduling policy for interference management. Most of the previous centralized works rely on precise instantaneous channel state information (CSI). In this paper, considering the impact of multirelay link interference on relay selection and dynamic spectrum sharing, we propose a fully distributed relay MAC scheme for wireless cooperative networks based on a Stackelberg game framework with only one-hop local CSI, where source nodes that have their own information to send act as leader users and where the others act as follower users. In this scenario, each relay node prices its spectrum resource to the corresponding source node to maximize its revenue. In addition, the proposed scheme helps not only source nodes to find relay nodes by channel gains and obtain an optimal system performance but relay nodes to maximize their revenue by asking a suitable resource price as well. The interactions between the sources and relays iteratively lead to a Stackelberg equilibrium, in which the cooperation system achieves high throughput and low transmission delay. Simulation results are presented to show the effectiveness of the proposed approach.

Joint Mode Selection and Spectrum Partitioning for Device-to-Device Communication: A Dynamic Stackelberg Game

Device-to-device (D2D) communication technology is a promising add-on component for future wireless networks to provide local area services with increased spectrum efficiency and improved user experience. Three modes (i.e., cellular mode, reuse mode, and dedicated mode) can be used for D2D communication. A potential D2D user equipment (UE) can select a communication mode and dynamically adapt the mode selection according to the performance and the cost. This is referred to as the user-controlled mode selection problem. Also, a base station (BS) needs to reserve a spectrum band for the dedicated mode of operation, which we refer to as spectrum partitioning. The optimal spectrum partitioning needs to consider the utility of the BS that depends on the distribution of the users' mode selection, which, in turn, is governed by the spectrum partitioning. To jointly address the problems of spectrum partitioning and user-controlled mode selection (which are cyclically dependent on each other), we propose a dynamic Stackelberg game framework in which the BS and the potential D2D UEs act as the leader and the followers, respectively. Specifically, the adaptive mode selection of potential D2D UEs is formulated as a follower evolutionary game, and an evolutionary stable strategy is considered to be the solution. The dynamic control of spectrum partitioning by the BS is formulated as a leader optimal control problem. We also extend the formulation by considering information delays in control and state. Numerical analysis is performed to evaluate the effectiveness of the proposed framework, which shows that although the mode selection is performed in a distributed and user-controlled manner, the dynamic spectrum partitioning can be viewed as an effective incentive mechanism to drive the user distribution close to the optimal one.

Comparisons of low carbon policies in supply chain coordination

This paper investigates the influence of low-carbon policies on channel coordination for a two-echelon supply chain consisting of one supplier and one retailer. Four different models are considered: the basic model, the carbon emission model, the carbon emission trading model and the carbon tax model. We find that the government policy on all carbon emission models is not universal among the firms as well as the customers. The carbon emission trading policy is always better than the carbon emission policy and the carbon tax policy when the allocated carbon emission quotas are greater than the carbon emissions. The carbon emission trading policy is proved to be an effective mechanism which can motivate the supply chain to reduce carbon emissions. Under certain conditions, the supply chain prefers the carbon emission trading policy with higher carbon price to other policies. In the framework of Stackelberg game with the supplier as the leader, for each carbon policy, the paper presents coordination mechanism with the all-unit wholesale quantity discount contract (AWQD). We analyze and compare the influence of low-carbon policies on channel coordination for the four low-carbon policies. Numerical experiments are conducted to examine our findings.

Resource Management for Device-to-Device Communications in Heterogeneous Networks Using Stackelberg Game

Device-to-device (D2D) communications and femtocell systems can bring significant benefits to users’ throughput. However, the complicated three-tier interference among macrocell, femtocell, and D2D systems is a challenging issue in heterogeneous networks. As D2D user equipment (UE) can cause interference to cellular UE, scheduling and allocation of channel resources and power of D2D communication need elaborate coordination. In this paper, we propose a joint scheduling and resource allocation scheme to improve the performance of D2D communication. We take UE rate and UE fairness into account by performing interference management. First, we construct a Stackelberg game framework in which we group a macrocellular UE, a femtocellular UE, and a D2D UE to form a two-leader one-follower pair. The cellular UE are leaders, and D2D UE is the follower who buys channel resources from the leaders. We analyze the equilibrium of the game and obtain solutions to the equilibrium. Second, we propose an algorithm for joint scheduling of D2D pairs based on their utility. Finally, we perform computer simulations to study the performance of the proposed scheme.

Optimizing production and inventory decisions in a supply chain with lot size, production rate and lead time interactions

Lead time decision involves interactions both supply side and demand side in a supply chain with different interests. A Stackelberg game framework is presented in this paper to model the interactions between a manufacturer and a retailer, in which the lead time demand is distribution free and only the mean and variance are known. Then, a minimax approach is applied to tackle the model, and an efficient iterative algorithm has been developed to solve the model. The numerical examples are employed to illustrate the solution procedure and analyze the double marginalization in the decentralized decision scenario. In addition, a transfer payment contract is proposed to coordinate the supply chain, through which the decentralized Stackelberg game decision can a results show that the contract can flexibly allocate the system’s cost between the two sides of the supply chain, and both sides in the supply chain become strictly better off through the collaboration.

Optimal Channel Choice under Stochastic Demand with Multiplicative and Additive Shocks

Based on the framework of Stackelberg game, we analyze and compare the optimal channel choices for the manufacturer and the retailer under consignment contract, when the demand is stochastic with uniformly distributed shock in multiplicative and additive forms respectively. We find that the price elasticity, range of demand fluctuation and the revenue sharing ratio affect the optimal channel choices for the manufacturer and the retailer differently under different forms of stochastic demand shocks.

A value-based approach to option pricing: The case of supply chain options

The pricing issue of supply chain options is generally considered in the Stackelberg game framework in the literature. Such a pricing scheme, however, is usually unacceptable to the follower in the game since it serves only the leader's interest. Different from the existing literature, we develop in this paper a value-based pricing scheme for supply chain options. We present the option pricing schemes for the cases of a single retailer and multiple retailers, respectively. The intuition behind our pricing schemes is to price the option based on the value inherent in the “option right”. As a result, our pricing schemes are more objective and fair, and consequently are more likely to be accepted by the contracting partners as compared with those that follow the Stackelberg game approach.

Hybrid Relay Forwarding and Interference Mitigation Mechanisms in Cooperative Cognitive Ad-Hoc Networks

In this paper, a cooperative cognitive ad-hoc network is considered where a primary user and secondary users coexist with an interference user. A hybrid cooperation mechanism is proposed which allows secondary users to cooperate with primary user by forwarding the interference user’s data as well as conventionally forwarding the primary user’s data. The proposed scheme provides a more flexible approach that the secondary user can select the relay method according to channel state information. The primary user would release a reasonable portion of spectrum in return for data relay (so the primary user could improves throughput), while the secondary users could earn more spectrum access rights. When there is an interference user, secondary users could choose a method to help primary users by relay forwarding or interference mitigation depending on its own channel quality. With an aim of maximizing primary user’s rate and minimizing the secondary users’ energy consumption, a Stackelberg game framework is introduced in which a primary user is modeled as the leader and multiple secondary users are modeled as followers. The secondary users control their power to cooperate with the primary user to optimize game utilization. The existence and uniqueness of the proposed game’s equilibrium is proved and a distributed iterative algorithm is designed to reach the game equilibrium. Numerical results show that the proposed hybrid relay forwarding and interference mitigation mechanism outperforms the single cooperation scheme when an interference user exists.

Cooperation in Transboundary Water Sharing with Issue Linkage: Game-Theoretical Case Study in the Volta Basin

AbstractThis paper investigates issue linkage of water and energy in transboundary water sharing agreements and evaluates how such issue linkages can enhance the scope of cooperation between upstream and downstream countries. In a case study on transboundary water sharing between Burkina Faso and Ghana, the main upstream and downstream riparians in the Volta Basin, the paper evaluates both the scope and sustainability of such cooperation based on issue linkage. In the framework of a static Stackelberg game with numerical analysis, it is found that the interdependency of countries can lead to efficient and effective solutions regarding water sharing. In the cooperation phase, Ghana has the opportunity to increase its water consumption for agriculture, which is currently restricted, while Burkina Faso benefits from discounted hydropower as a compensation for restricting its water consumption. In such a case, the cooperation is mutually beneficial and stable. However, such interdependency may not be sustaina...

Manufacturer–retailer supply chain coordination: A bi-level programming approach

This paper investigates a multi-product manufacturer–retailer supply chain where demand of each product is jointly influenced by price and advertising expenditure. We propose a Stackelberg game framework under two power scenarios. In the first, we consider the traditional approach where the manufacturer is the leader. In the latter, we allow the retailer to act as the dominant member of the supply chain. Bi-level programming approach is applied to find the optimal equilibrium prices, advertising expenditures and production policies; then several solution procedures, including imperialist competitive algorithm, modified imperialist competitive algorithm, and evolution strategy are proposed. Finally numerical experiments are carried out to evaluate the effectiveness of models as well as solution procedures.

RFID Tag Cost Sharing in the Retail Supply Chain

In this research, we study some of the operational benefits of item-level radio frequency identification (RFID), and how these benefits may affect the dynamics of the retailer-manufacturer interaction. We describe a retail operation with backroom and shelf stock under the assumption of multiple replenishment and sales periods, where backroom stock is replenished according to a periodic review order-up to policy and shelf stock is replenished continually from the backroom. In this environment, retail shelves are outfitted with RFID readers to continually monitor the remaining stock on the shelves and issue low-stock and replenishment alerts to store personnel so that shelves can be replenished from the store backroom before actual sales are lost at the shelf. We are interested in the dynamics between retailer and manufacturer with respect to the cost of item-level tagging the products. Of interest is the way in which the cost of tagging the product is divided among the two supply chain partners. To do this, we investigate a supply chain in which power is distributed asymmetrically among manufacturer and retailer. This interaction is modeled using the Stackelberg game framework. From an analysis of this framework, we derive several properties of interest, relating to the appropriate division of tagging cost as well as to a life-cycle centric view of RFID implementations.

Optimal coordinated supply chain strategy with price and time sensitive demand

In this study, inventory models are developed for coordinated supply chain using Stackelberg game framework. In the proposed model, customer demand is assumed to be price and time sensitive. The buyer attempts to adjust retail selling prices by charging premium or offering discount to the floor selling price depending upon the optimistic or declining market conditions. The aim of this research paper is to analyse the optimal pricing policy that maximises total profit for both the players under the principles of coordination, and competition. Some numerical examples are given to study the model. The results show that the vendor gets more advantage when the collaborative model is applied and the buyer’s profit is bigger in the Stackelberg game model than the collaborative model.

Spectrum Leasing to Cooperating Secondary Ad Hoc Networks

The concept of cognitive radio (or secondary spectrum access) is currently under investigation as a promising paradigm to achieve efficient use of the frequency resource by allowing the coexistence of licensed (primary) and unlicensed (secondary) users in the same bandwidth. According to the property-rights model of cognitive radio, the primary terminals own a given bandwidth and may decide to lease it for a fraction of time to secondary nodes in exchange for appropriate remuneration. In this paper, we propose and analyze an implementation of this framework, whereby a primary link has the possibility to lease the owned spectrum to an ad hoc network of secondary nodes in exchange for cooperation in the form of distributed space-time coding. On one hand, the primary link attempts to maximize its quality of service in terms of either rate or probability of outage, accounting for the possible contribution from cooperation. On the other hand, nodes in the secondary ad hoc network compete among themselves for transmission within the leased time-slot following a distributed power control mechanism. The investigated model is conveniently cast in the framework of Stackelberg games. We consider both a baseline scenario with full channel state information and information-theoretic transmission strategies, and a more practical model with long-term channel state information and randomized distributed space-time coding. Analysis and numerical results show that spectrum leasing based on trading secondary spectrum access for cooperation is a promising framework for cognitive radio.

Stackelberg Routing in Atomic Network Games

We consider network games with atomic players, which indicates that some players control a positive amount of flow. Instead of studying Nash equilibria as previous work has done, we consider that players with considerable market power will make decisions before the others because they can predict the decisions of players without market power. This description fits the framework of Stackelberg games, where those with market power are leaders and the rest are price-taking followers. As Stackelberg equilibria are difficult to characterize, we prove bounds on the inefficiency of the solutions that arise when the leader uses a heuristic that approximate its optimal strategy.