Multi-leader Multi-follower Stackelberg Game Research Articles

Bi-level Multi-leader Multi-follower Stackelberg Game Model for Multi-energy Retail Package Optimization

Bi-level Multi-leader Multi-follower Stackelberg Game Model for Multi-energy Retail Package Optimization

Joint Slot Scheduling and Power Allocation for Throughput Maximization of Clustered UASNs

In the last decades, independent consideration of underwater acoustic medium access control (MAC) layer has received much attention for designing a reliable data transmission protocol. Although it can simplify the system design, it is often insufficient for the enhancement of overall system performance. The focus of this paper is on the cross-layer optimization to maximize the network throughput (NT) of clustered underwater acoustic sensor networks (UASNs) by jointly optimizing the sensor nodes’ slot scheduling and power allocation. The formulated problem is a mixed integer non-linear programming problem, which is NP-hard. An alternating-optimization-based centralized algorithm is proposed first to solve it, which can achieve the best NT performance but at the price of high complexity. Therefore, a multi-leader multi-follower Stackelberg game based distributed algorithm is also proposed to achieve a better tradeoff between system performance and complexity. Simulation results demonstrate that our proposed schemes considering the information causality constraint have a better NT performance than those without a “systematic” consideration over such joint optimization, like CMS-MAC algorithm.

A Distributed Pricing Strategy for Edge Computation Offloading Optimization in Autonomous Driving

The increase of on-vehicle applications has brought explosive computation demands to autonomous vehicles and overwhelmed their limited onboard resources. Edge computing can offload application load and effectively alleviate this problem. However, the introduction of edge computing faces significant challenges, including the considerable amount of resource contention due to the scarcity of edge resources and the competition among edge computing resource providers to earn users' services requests. We notice that the problem is not purely technical as solutions for these two problems can become conflicting to each other. In this paper, we propose a distributed pricing strategy to achieve full use of computing resources at the edge and maximize the revenue of service operators, both with guaranteed quality-of-service of on-vehicle applications. More specifically, we first use the multi-leader multi-follower Stackelberg game theory to model the pricing of on-vehicle task offloading under edge computing. Next, we propose a distributed pricing strategy to enable edge servers to adjust their local price distributions so that edge servers can bargain with offloading requesters independently. Experimental results confirm that the proposed distributed pricing strategy can provide more optimized server computing resource utilization while guaranteeing the performance of in-vehicle applications.

Toward Personalized Federated Learning Via Group Collaboration in IIoT

Despite the rapid growth of successful examples of Federated Learning (FL), it faces the heterogeneity of data, models, and devices in emerging applications of Industrial Internet of Things (IIoT). Existing efforts mainly focus on training multiple personalized models by adopting a global, cluster, or pairwise fashion. However, the global collaboration doesn't work well in case of the non-IID data distribution, cluster collaboration is often inefficient due to the single cluster pattern and high computational cost, and pairwise collaboration incurs the limitations of collaboration scope and communication efficiency. To address the problems, we propose a novel Personalized FL (PFL) framework with the game-theoretic insights, called group collaboration, to overcome the shortcomings of status quo. Specifically, we first formulate the group collaboration in PFL as a multi-leader multi-follower Stackelberg game, and then develop an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> -better response to efficiently characterize its unique equilibrium through cautiously proposing a potential function. Since the existing equilibrium may not be optimal, we further design a Robin Hood mechanism by using the idea of transferable utility to improve the performance of the training model. Meanwhile, we also prove that the new mechanism is sustainable and can converge to a stable state with an upper bound of the training loss. Last, extensive experiments on a simulated dataset and four real-world datasets demonstrate the superiority of our proposed approach compared to the state-of-the-art.

Demand Response Flexibility Potential Trading in Smart Grids: A Multileader Multifollower Stackelberg Game Approach

The value of demand response (DR) for improving the operational efficiency of smart grids has been widely recognized. To further explore the potential DR flexibility, this article presents a novel framework for DR resource trading between multiple service providers (SPs) and end customers, in which SPs are supposed to offer diversified incentives to a resource trading center (RTC) while anticipating responses from the demand side. Distinguished from previous studies, in this work each end customer is endowed the authority to simultaneously trade with multiple SPs with the intention of maximizing their net utilities. The trading process between SPs and customers is demonstrated by a multileader multifollower Stackelberg game, due to its superiority of modeling problems with hierarchical decision-making behaviors. To solve the formulated game, an exact potential function is proposed to help determine the unique Nash equilibrium (NE) among SPs, which serves as the cornerstone for further deriving the Stackelberg equilibrium (SE), i.e., the ultimate outcome of the resource trading process. Simulation results verified that the DR flexibility was significantly increased compared with the case when there is only one SP responsible for the entire trading on behalf of all the end customers. Moreover, the proposed approach is also able to bring extra benefits for both SPs and customers in terms of net profit and net utility value.

Pricing and Budget Allocation for IoT Blockchain With Edge Computing

Attracted by the inherent security and privacy protection of the blockchain, incorporating blockchain into Internet of Things (IoT) has been widely studied in these years. However, the mining process requires high computational power, which prevents IoT devices from directly participating in blockchain construction. For this reason, edge computing service is introduced to help build the IoT blockchain, where IoT devices could purchase computational resources from the edge servers. In this paper, we consider the case that IoT devices also have other tasks that need the help of edge servers, such as data analysis and data storage. In this scenario, IoT devices will allocate their limited budgets to purchase different resources from different edge servers, such that their profits can be maximized. Moreover, edge servers will set "best" prices such that they can get the biggest benefits. We model the interaction between edge servers and IoT devices as a multi-leader multi-follower Stackelberg game, whose objective is to reach the Stackelberg Equilibrium (SE). We prove the existence and uniqueness of the SE point, and design efficient algorithms to reach the SE point. In the end, we verify our model and algorithms by performing extensive simulations.

Edge Resource Pricing and Scheduling for Blockchain: A Stackelberg Game Approach

Blockchain came to prominence as the distributed ledger underneath Bitcoin, which protects the transaction histories in a fully-connected, peer-to-peer network. The blockchain mining process requires high computing power to solve a Proof-of-Work (PoW) puzzle, which is hard to implement on users’ mobile devices. So these miners may leverage the edge/cloud service providers (ESPs/CSP) to calculate the PoW puzzle. The existing edge-assisted blockchain networks assumed that all ESPs have a uniform propagation delay, which is unrealistic. In this article, we consider a more practical scene where ESPs locate in diverse positions of the blockchain network, which causes different propagation delays when supporting the computation of the PoW puzzle. Additionally, these ESPs connect to a remote CSP for resource scheduling when the computing tasks exceed their maximum capacity. The blockchain mining process generally involves complicated competition and games among CSP, ESPs, and miners. Each service provider focuses on how to determine his resource price so that he can maximize his utility. According to the set resource price, each miner concentrates on scheduling his resource requests for each ESP to maximize individual personal utility, which depends on ESPs’ resource price and propagation delays. We first model such a resource pricing and scheduling problem as a three-stage multi-leader multi-follower Stackelberg game and aim at finding the Stackelberg equilibrium. Then, we analyze the subgame optimization problem in each stage and propose an iterative algorithm based on backward induction to achieve the Nash equilibrium of the Stackelberg game. Finally, extensive simulations are conducted to verify the significant performance of the proposed solution.

Stackelberg game-based dynamic resource trading for network slicing in 5G networks

Network slicing (NS) has been envisioned as the main technology in 5G to accommodate different virtualized operators with versatile service requirements, on a common substrate infrastructure. NS has come to radically reform the interaction among different entities in the resource sharing market, where resource is exchanged for monetary gains as a way of ensuring efficient resource utilization. However, resource exchange is only attractive to entities if they are able to achieve their respective benefits in a win–win situation. In this paper, we design an economic model that analyzes the pricing and purchasing interaction between multiple mobile virtual network operators (MVNOs) and their respective users for resource trading in NS. We formulate the pricing and purchasing problem as a two-stage multi-leader multi-follower (MLMF) Stackelberg game where the MVNOs as leaders set their unit price first, and then users as followers respond by determining their purchasing volume. Then, we theoretically prove the existence and uniqueness of a Nash equilibrium (NE). To obtain an optimal dynamic pricing solution for the MVNOs, we transform the game-based optimization problem into a stochastic Markov decision process (MDP) problem and propose a method based on multi-agent dueling deep Q-Network (DQN) algorithm. Simulation results show that the proposed algorithm achieves convergence under competitive pricing scheme (CPS) and independent pricing scheme (IPS), while ensuring high MVNOs’ profit and users’ utility at acceptable levels. In terms of cumulative profits, the proposed dueling DQN-based pricing algorithm achieves percentage gains of 15.3%, 30.4%, and 71.4% against Q-learning-based pricing, premium pricing, and undercut pricing algorithms as benchmarks.

Multi-Operator Dynamic Spectrum Sharing for Wireless Communications: A Consortium Blockchain Enabled Framework

To enable secure and efficient dynamic spectrum sharing (DSS) with guaranteed revenue and quality of service (QoS) in future wireless communications, we present a consortium blockchain based DSS framework, where the regulators supervise the whole process of DSS, and thus the revenue of each participant can be guaranteed. Each mobile network operator (MNO) on the chain can adaptively act as a spectrum provider or spectrum requestor based on their demand, and the spectrum resource allocation is recorded on the chain with a smart contract. The optimal spectrum pricing and buying strategies are solved based on a multi-leader multi-follower (MLMF) Stackelberg game model, and the equilibrium is solved with the proposed algorithm. We then build a prototype with Hyperledger Fabric consortium blockchain, and the average latency is evaluated. Simulations and prototype evaluations validate the feasibility of blockchain based DSS and show that the average latency increase with the participants, which provides useful insights for real applications.

Peer-to-peer energy trading in energy local area network considering decentralized energy routing

Peer-to-peer (P2P) energy trading is perceived as a promising energy management mechanism for decentralized renewable energy sources. The concept of energy local area network (e-LAN) is proposed as a new system framework for future microgrids to facilitate P2P trading where the end-to-end power delivery is achieved by energy routing. Decentralized P2P trading in e-LAN requires a perfectly competitive market and flexible end-to-end power delivery. In this paper, a new P2P trading model incorporating decentralized energy routing is proposed for e-LAN. The proposed model is composed of a P2P energy market and a loss compensation market. In the P2P energy market, a tripartite graph model is proposed to represent transactions where trading decisions and energy routing are jointly considered for each participant to pursue its optimal benefit. Considering the size problem and nonlinear weights of the tripartite graph, an extended depth-first branch-and-bound algorithm is proposed to prune low-efficiency paths. Based on the pruned tripartite graph, the competitive P2P market is captured by a multi-leader multi-follower Stackelberg game model. A loss compensation market is established to coordinate energy routing paths planned in a decentralized manner. By means of setting the price for utilizing each transmission line, the loss compensation market avoids network congestion and ensure a normal operation of e-LAN. Simulation results show that the proposed model can bring higher utilities for P2P participants compared with the existing P2P trading models in e-LAN. Additionally, the effectiveness of the proposed model in resolving path conflicts in a decentralized fashion and improving computation efficiency, are verified.

Joint Task Offloading and Dispatching for MEC With Rational Mobile Devices and Edge Nodes

Multi-access Edge Computing has come forth as a promising paradigm to provide low-latency computing service to mobile end users. Its basic idea is to deploy computation resources at the edge of core networks such as wireless access points, and then users can offload their tasks to nearby edge nodes for processing. Plenty of works have well studied the task offloading problem, aiming to reduce task completion delays. Also, a few recent works have focused on task dispatching among edge nodes to balance their workloads and improve resource utilization. In this work, we jointly consider the task offloading and dispatching problem in an edge computing system with interconnected access points. Furthermore, we assume both end devices and access points are rational, which only care about their own benefits. To solve the joint problem, we firstly formulate it as a multi-leader multi-follower Stackelberg game, and rigorously prove the existence of a Stackelberg equilibrium. Then, we propose two algorithms for task offloading and dispatching, respectively. Extensive simulations are conducted to show the superiority of our proposed approach. We also demonstrate that an upper bound with a constant approximation ratio is achieved by our approach.

Price and Risk Awareness for Data Offloading Decision-Making in Edge Computing Systems

The proliferation of multiaccess edge computing (MEC) paradigm has created a challenging multiuser–multiserver–multiaccess edge computing competitive environment, which brings the problem of data offloading decision-making to the forefront of research. In this article, we address this issue while jointly studying the impact of the user behavioral characteristics and the MEC servers pricing policies on determining the optimal user data offloading strategies. Prospect theory is exploited to reflect the user satisfaction and subjectivity from the data offloading, while the MEC servers’ probability of failure owing to the potential overexploitation by the users, is modeled via the theory of tragedy of the commons. A multileader multifollower Stackelberg game is formulated among the MEC servers (leaders) and the users (followers), to determine the servers’ optimal pricing policies and the users’ optimal data offloading strategies. The users’ data offloading decision-making is formulated as a noncooperative game among them and a Nash equilibrium is determined, while the MEC servers’ optimal computing service prices are obtained either through a semiautonomous game-theoretic approach, or through a fully autonomous reinforcement learning-based approach. The performance evaluation and demonstration of the superiority of the proposed framework against other benchmarking alternatives is achieved via modeling and simulation.

A bilevel game-theoretic decision-making framework for strategic retailers in both local and wholesale electricity markets

This paper proposes a bilevel game-theoretic model for multiple strategic retailers participating in both wholesale and local electricity markets while considering customers’ switching behaviors. At the upper level, each retailer maximizes its own profit by making optimal pricing decisions in the retail market and bidding decisions in the day-ahead wholesale (DAW) and local power exchange (LPE) markets. The interaction among multiple strategic retailers is formulated using the Bertrand competition model. For the lower level, there are three optimization problems. First, the welfare maximization problem is formulated for customers to model their switching behaviors among different retailers. Second, a market-clearing problem is formulated for the independent system operator (ISO) in the DAW market. Third, a novel LPE market is developed for retailers to facilitate their power balancing. In addition, the bilevel multi-leader multi-follower Stackelberg game forms an equilibrium problem with equilibrium constraints (EPEC) problem, which is solved by the diagonalization algorithm. Numerical results demonstrate the feasibility and effectiveness of the EPEC model and the importance of modeling customers’ switching behaviors. We corroborate that incentivizing customers’ switching behaviors and increasing the number of retailers facilitates retail competition, which results in reducing strategic retailers’ retail prices and profits. Moreover, the relationship between customers’ switching behaviors and welfare is reflected by a balance between the electricity purchasing cost (i.e., electricity price) and the electricity consumption level.

Incentive mechanism for competitive edge caching in 5G-enabled Internet of things

The fifth generation (5G) of cellular networks provides the enabling environment for the Internet of Things (IoT) applications. Hence, the vast proliferation of 5G-enabled IoT devices and services led to an overwhelming growth of data traffic that could saturate the core network’s backhaul links. Nowadays, caching is an unavoidable technique to solve this issue, whereby popular contents are stored on edge nodes near to end-users. There exist several initiatives to motivate caching actors for improving the caching process, but not designed for the real-world competitive caching market. In this work, we propose an incentive caching strategy in a 5G-enabled IoT network by considering a completely competitive caching scenario with multiple 5G mobile network operators (MNOs) and multiple content providers (CPs). The MNOs manage a set of edge caches on their base stations and they are competing to fill these caching resources, while the CPs detain a set of popular contents and are in conflict to rent the MNOs’ caches. Each MNO aims to maximize its monetary profit and offload its backhaul links, as each CP aims to improve the quality of experience (QoE) of its end-users. Then, we formulate a multi-leader multi-follower Stackelberg game to model the interaction between MNOs and CPs and define the different players’ utilities. Subsequently, we propose an iterative algorithm based on the convex optimization method to investigate the Stackelberg equilibrium. Finally, the numerical results of the different experimentations demonstrate that our game-based incentive strategy can significantly alleviate the backhaul links while improving the user QoE.

An Architecture for Distributed Energies Trading in Byzantine-Based Blockchains

With the development of smart cities, not only are all corners of the city connected to each other, but also connected from city to city. They form a large distributed network together, which can facilitate the integration of Distributed Energy Stations (DESs) and corresponding smart aggregators. Nevertheless, because of potential security and privacy protection arising from trustless energies trading, how to make such energies trading go smoothly is a tricky challenge. In this paper, we propose a blockchain-based multiple energies trading (B-MET) system for secure and efficient energies trading by executing a smart contract we design. Because energies trading requires the blockchain in B-MET system to have high throughput and low latency, we design a new byzantine-based consensus mechanism (BCM) based on node&#x2019;s credit to improve efficiency for the consortium blockchain under the B-MET system. Then, we take combined heat and power (CHP) system as a typical example that provides distributed energies. We quantify their utilities and model the interactions between aggregators and DESs in a smart city by a novel multi-leader multi-follower Stackelberg game. It is analyzed and solved by reaching Nash equilibrium between aggregators, which reflects the competition between aggregators to purchase energies from DESs. In the end, we conduct plenty of numerical simulations to evaluate and verify our proposed model and algorithms, which demonstrate their correctness and efficiency completely.

EDCSuS: Sustainable Edge Data Centers as a Service in SDN-Enabled Vehicular Environment

Cloud computing has emerged as one of the popular technologies which provide on-demand services to the end users. Such services are hosted by massive geo-distributed data centers (DCs). Nowadays, connected vehicles in a smart city can also avail cloud services through Internet using cellular technologies. But, the advent of 5G technology has posed challenges for DCs such as-low latency and higher data rate requirements. To handle these challenges, edge-DCs (EDCs) can be deployed across a smart city to provide low latency services to the connected vehicles. In lieu of this, in this paper, EDCSuS: Sustainable EDC as a service framework in software defined vehicular environment is proposed. In EDCSuS, first, a software defined controller handles the incoming requests and suggest an optimal flow path. Second, a multi-leader multi-follower Stackelberg game is presented for resource allocation. Third, to improve the resource utilization, a cooperative resource sharing scheme is designed, thereby minimizing the energy consumption of servers in the EDCs. Lastly, a caching scheme is presented to avert excessive energy consumption for retracing the lost link due to vehicular mobility. The efficacy of the proposed scheme has been evaluated using extensive simulations with respect to various parameters. The results obtained prove the effectiveness of EDCSuS.

Shared-constraint approach for multi-leader multi-follower game of generation companies participating in electricity markets with carbon emission trading mechanism

There is a high degree of overlap between market entities covered by the carbon emission trading (CET) market and electricity market, and the two markets are closely related. Therefore, it is of great significance to analyze the impact of the CET market mechanism on the bidding strategy of generation companies (GENCOs) and electricity market clearing results. In this paper, the problem of GENCOs participating in both the day-ahead and real-time balancing electricity market within the CET mechanism is studied as a multi-leader multi-follower (MFML) Stackelberg game problem. The GENCOs are considered as leaders in the game who decide on the submitted bid and offer in terms of price and quantity to maximize their expected profit in the market, while both the clearing problems of day-ahead and real-time markets are considered as followers on the lower level. In order to expand the Nash equilibrium of the considered MFML game, the shared-constraint approach is applied to modify this problem. Two typical Nash equilibria of the proposed MLMF game are analyzed and discussed. Finally, the results of the simulations conducted on a modified IEEE 39-bus system and a real 2778-bus system indicate that GENCOs tend to submit bids with a higher price in the market under the global Nash equilibrium solution. Within the CET mechanism, the overall market clearing share of the gas-fired units increases from 21.76% to 18.1%–32.33% and 19.51%, at valley and peak loads, respectively. Thus, the operation of the CET market will make low-emission units more competitive in the electricity market.

A Novel Joint Dataset and Incentive Management Mechanism for Federated Learning Over MEC

In this study, to reduce the energy consumption for the federated learning (FL) participation of mobile devices (MDs), we design a novel joint dataset and incentive management mechanism for FL over mobile edge computing (MEC) systems. We formulate a Stackelberg game to model and analyze the behaviors of FL participants, referred to as MDs, and FL service providers, referred to as MECs. In the proposed game, each MEC is the leader, whereas the MDs are followers. As the leader, to maximize its own revenue by considering the trade-off between the cost of providing incentives and the estimated accuracy attained from an FL operation, each MEC provides full incentives to the MDs for the participation of each FL task, as well as the target accuracy level for each MD. The suggested total incentives are allocated over MDs’ proportion to the amount of dataset applied for local training, which indirectly affects the global accuracy of the FL. Based on the suggested incentives, the MDs determine the amount of dataset used for the local training of each FL task to maximize their own payoffs, which is defined as the energy consumed from FL participation and the expected incentives. We study the economic benefits of the joint dataset and incentive management mechanism by analyzing its hierarchical decision-making scheme as a multi-leader multi-follower Stackelberg game. Using backward induction, we prove the existence and uniqueness of the Nash equilibrium among MDs, and then examine the Stackelberg equilibrium by analyzing the leader game. We also discuss extensions of the proposed mechanism where the MDs are unaware of explicit information of other MD profiles, such as the weights of the revenue as a practical concern, which can be redesigned into the Stackelberg Bayesian game. Finally, we reveal that the Stackelberg equilibrium solution maximizes the utility of all MDs and the MECs.

A Multi-Leader Multi-Follower Stackelberg Game for Coalition-Based UAV MEC Networks

In this letter, we investigate the joint optimization of computation offloading, channel allocation and position deployment problem for coalition-based unmanned aerial vehicle (UAV) mobile edge computing networks. To characterize the hierarchical offloading feature in coalition-based UAV network, we propose the hierarchical framework and formulate a discrete multi-leader multi-follower energy minimization Stackelberg game. In addition, we prove that the multi-leader subgame and multi-follower subgame are exact potential games with Nash equilibrium. Then the existence of Stackelberg equilibrium (SE) is guaranteed. The spatial adaptive play-best response based hierarchical iterative learning (SAP-BRHIL) algorithm is proposed to achieve the SE. The simulation results show that the proposed SAP-BRHIL algorithm can achieve the lowest network energy consumption compared with some existing approaches.

Hierarchical coordinated anti-jamming channel access in clustering networks: a multi-leader multi-follower Stackelberg game approach

This paper mainly investigates the multi-user coordinated anti-jamming problem in clustering communication networks. In such kinds of networks, there exist multiple clusters and multiple users who communicate with their receivers simultaneously. Besides, a malicious jammer persistently attacks channels with wide-band and dynamic changing jamming signals. To cope with these challenges brought by the large-scale clustering network and the dynamic wide-band jamming, a hierarchical coordinated anti-jamming approach is proposed, and a multi-leader multi-follower Stackelberg game is introduced to model the anti-jamming problem. In detail, cluster heads act as leaders, and select available frequency bands to avoid jamming attacks, while users in each cluster act as followers and select corresponding channels distributedly and independently. Moreover, it is proved that there exist multiple Stackelberg equilibriums (SEs) in the proposed game. To obtain SEs, a hierarchical coordinated anti-jamming channel access (HCACA) algorithm is designed. Simulation results illustrate that the proposed approach is effective to cope with the dynamic wide-band jamming attacks. Furthermore, it is also depicted that the proposed approach outperforms the distributed anti-jamming comparative approach in terms of convergence speed.