Stackelberg Leader-follower Game Research Articles

Linear-Quadratic Mixed Stackelberg–Nash Stochastic Differential Game with Major–Minor Agents

In this paper, we study a controlled linear-quadratic-Gaussian large population system combining three types of interactive agents mixed, which are respectively, major leader, minor leaders, and minor followers. In reality, they may represent three typical types of participants involved in market price formation: major supplier, minor suppliers and minor producers. The Stackelberg–Nash–Cournot (SNC) approximate equilibrium is derived from the combination of a major–minor mean-field game (MFG) and a leader–follower Stackelberg game. Although all agents are of forward states in that only initial conditions are specified in their dynamics, our SNC analysis provides an MFG framework that is naturally in a forward–backward state in that both initial and terminal conditions are specified. This result differs from those reported in the literature on standard MFG frameworks, mainly as a result of the adoption of a Stackelberg structure. Through variational analysis, the consistency condition system can be represented by some fully-coupled forward–backward-stochastic-differential-equations with a high-dimensional block structure in an open-loop case. To sufficiently address the related solvability, we also derive the feedback form of the SNC approximate. equilibrium strategy via some coupled Riccati equations. Our study includes various mean-field game models as its special cases.

Network-Aware Demand-Side Management Framework With A Community Energy Storage System Considering Voltage Constraints

This paper studies the feasibility of integrating a community energy storage (CES) system with rooftop photovoltaic (PV) power generation for demand-side management of a neighbourhood while maintaining the distribution network voltages within allowed limits. To this end, we develop a decentralized energy trading system between a CES provider and users with rooftop PV systems. By leveraging a linearized branch flow model for radial distribution networks, a voltage-constrained leader-follower Stackelberg game is developed wherein the CES provider maximizes revenue and the users minimize their personal energy costs by trading energy with the CES system and the grid. The Stackelberg game has a unique equilibrium at which the CES provider maximizes revenue and the users minimize energy costs at a unique Nash equilibrium. A case study, with realistic PV power generation and demand data, confirms that the energy trading system can reduce peak energy demand and prevent network voltage excursions, while delivering financial benefits to the users and the CES provider. Further, simulations highlight that, in comparison with a centralized system, the decentralized energy trading system provides greater economic benefits to the users with less energy storage capacity.

Data-Driven Game-Based Pricing for Sharing Rooftop Photovoltaic Generation and Energy Storage in the Residential Building Cluster Under Uncertainties

In this article, a novel machine learning based data-driven pricing method is proposed for sharing rooftop photovoltaic (PV) generation and energy storage in an electrically interconnected residential building cluster (RBC). In the studied problem, the energy sharing process is modeled by the leader-follower Stackelberg game where the owner of the rooftop PV system is responsible for pricing self-generated PV energy and operating ES devices. Meanwhile, local electricity consumers in the RBC choose their energy consumption with the given internal electricity prices. To track the stochastic rooftop PV panel outputs, the long short-term memory network based rolling-horizon prediction function is developed to dynamically predict future trends of PV generation. With system information, the predicted information is fed into a Q-learning based decision-making process to find near-optimal pricing strategies. The simulation results verify the effectiveness of the proposed approach in solving energy sharing problems with partial or uncertain information.

Time-Dependent Pricing for Bandwidth Slicing Under Information Asymmetry and Price Discrimination

Due to the bursty nature of Internet traffic, network service providers (NSPs) are forced to expand their network capacity in order to meet the ever-increasing peak-time traffic demand, which is however costly and inefficient. How to shift the traffic demand from peak time to off-peak time is a challenging task for NSPs. In this paper, we study the implementation of time-dependent pricing (TDP) for bandwidth slicing in software-defined cellular networks under information asymmetry and price discrimination. Congestion prices indicating real-time congestion levels of different links are used as a signal to motivate delay-tolerant users to defer their traffic demands. We formulate the joint pricing and bandwidth demand optimization problem as a two-stage Stackelberg leader-follower game. Then, we investigate how to derive the optimal solutions under the scenarios of both complete and incomplete information. We also extend the results from the simplified case of a single congested link to the more complicated case of multiple congested links, where price discrimination is employed to dynamically adjust the price of each congested link in accordance with its real-time congestion level. Simulation results demonstrate that the proposed pricing scheme achieves superior performance in increasing the NSP’s revenue and reducing the peak-to-average traffic ratio (PATR).

Toward sustainable optimization with stackelberg game between green product family and downstream supply chain

Green products are increasingly considered by companies, owing to the significant attention of government regulations, customers’ requests and competitors. Here, we deal with Green Product Families (GPFs) by selecting green components, modules and products which are produced based on the assembling to order (ATO) approach to cover diverse customer needs. Designing a GPFs is important but not sufficient for sustainable optimization. In fact, we need to simultaneously consider the supply chain of a GPF to control the pollution generated in the downstream supply chain. For a sustainable optimization approach, this joint configuration is usually structured based on economic, environmental and social criteria, which are often conflicting. Maximizing the total profit, maximizing the product greenness and minimizing the total supply chain cost with environmental considerations constitute our main objectives. We apply the Leader-Follower Stackelberg game in order to present a joint configuration of the GPF and its green supply chain (GSC). Maximizing the total profit (an economic criterion) and maximizing product greenness (a social criterion) are the two objectives of the leader problem to attain the GPF. This is done by determining the optimal selection of components, modules, and product variants. The follower of the joint problem seeks to configure the supply chain by minimizing the GSC costs considering carbon emissions (an environmental criterion). This includes the optimal selection of suppliers, manufacturers, the assembly plant, distribution centers, and retailers. A bi-level multi-objective linear programming problem (B-MOLP) is used to model the Stackelberg game of the GPF-GSC. A new particle swarm optimization algorithm, named as bi-level multi-objective PSO (B-MOPSO), is developed to solve the proposed bi-level multi-objective model. To show the validity of the proposed model and the efficiency of our algorithm, a case study at a mobile phone company is worked through. Finally, certain results with some managerial implications are obtained through a sensitivity analysis.

Optimizing the selection and scheduling of multi-class projects using a Stackelberg framework

One of the major causes of non-recurrent traffic congestion in urban areas is the implementation of transport infrastructure projects on city roads. The seeming ubiquity of work zones in cities causes road user frustration and safety hazards, and public relations problems for the transport agency. For this reason, transport agencies seek strategic ways to not only select urban projects but also schedule them in a manner that minimizes the effort associated with these functions. In other words, they seek to exploit the synergies between the tasks of project selection and project scheduling while duly accommodating the project interdependencies. This study introduces a general framework that simultaneously and optimally selects and schedules urban road projects subject to budgetary constraints over a given planning horizon. The project classes considered in this study are lane addition, new road construction, and road maintenance. Through a mimicry of the classic Stackelberg leader-follower game, this problem is formulated herein as a bi-level program. In the upper level, the leader (transport agency decision-makers) determines an optimal set of projects from a larger pool of candidate projects and decides an optimal schedule for their implementation. In the lower level, the followers (road users) seek to minimize their travel delays based on the two decisions made by the leader in the upper level. The numerical experiments show that if the decision-makers do not consider the peri-implementation capacity reduction, the resulting set of selected projects and their construction schedule can lead to significant travel delay cost for the road users.

Co-reconfiguration of product family and supply chain using leader–follower Stackelberg game theory: Bi-level multi-objective optimization

This article deals with product Family: a group of products with similar modules produced based on assembling to order (ATO) approach to cover diverse customer needs. The demand level and the customer requirements of these products are dynamically changing, which necessitate a novel model for co-reconfiguration of the product family (PF) and the supply chain (SC). Therefore, this article aims to apply Leader–follower Stackelberg Game Theory in order to present a co-reconfiguration of PF and SC based on three objectives: maximizing the total profit, maximizing customer utility and minimizing the supply chain cost in a bi-level structure. Maximizing the total profit and maximizing customer utility are the two objectives of the Leader problem for product family reconfiguration, which results in the optimal selection of components, modules, and product variants. The upper-level problem is considered as a multi-objective problem with the aforementioned two objectives. The lower level of this problem intends to reconfigure the supply chain with the objective of minimizing the supply chain costs, and therefore, to reach the optimal selection of suppliers, manufacturers, assembly plant, distribution centers, and retailers. A bi-level multi-objective linear programming problem (B-MOLP) is used to model the game of the leader–follower. A new particle swarm optimization algorithm, called bi-level multi-objective PSO (B-MOPSO), is developed to solve the proposed bi-level multi-objective model. To show the validity of the proposed model and the efficiency of our algorithm, a case study at a mountain bike industry is investigated. Finally, results in some managerial implications are obtained through sensitivity analysis.

An Incentive-Compatible Energy Trading Framework for Neighborhood Area Networks With Shared Energy Storage

Here, a novel energy trading system is proposed for demand-side management of a neighborhood area network (NAN) consisting of a shared energy storage (SES) provider, users with non-dispatchable energy generation, and an electricity retailer. In a leader-follower Stackelberg game, the SES provider first maximizes their revenue by setting a price signal and trading energy with the grid. Then, by following the SES provider's actions, the retailer minimizes social cost for the users, i.e., the sum of the total users' cost when they interact with the SES and the total cost for supplying grid energy to the users. A pricing strategy, which incorporates mechanism design, is proposed to make the system incentive-compatible by rewarding users who disclose true energy usage information. A unique Stackelberg equilibrium is achieved where the SES provider's revenue is maximized and the user-level social cost is minimized, which also rewards the retailer. A case study with realistic energy demand and generation data demonstrates 28\%~-~45\% peak demand reduction of the NAN, depending on the number of participating users, compared to a system without SES. Simulation results confirm that the retailer can also benefit financially, in addition to the SES provider and the users.

Capacity Planning of Micro Energy Grid Using Double-Level Game Model of Environment-Economic Considering Dynamic Energy Pricing Strategy

Multi-energy unified planning is difficult because of the complex conflicting relationship between the coupling and complementary interaction of multiple forms of energy in micro energy grids (MEGs). Conflicting relationships between the economy and the environment as well as the impact of uncertain energy prices must be considered during MEG planning. To address these problems, this paper proposes a two-level game with an environment-economic planning model that considers dynamic energy pricing strategies. This model consists of an upper environment-economic planning level based on a multi-strategy evolution game considering players' bounded rationality and a lower dynamic energy pricing level, including the MEG operator-user leader-follower Stackelberg game. Simultaneously, based on the energy hub theory, a multi energy coupling matrix is established for a MEG and includes electricity, gas, heat, and cooling. The evolutionary stability strategy (ESS) of the planning results is analyzed using the replicator dynamic equation of the evolutionary game, and the existence of the Nash equilibrium is proven for the dynamic energy pricing of Stackelberg games. Finally, the effectiveness of the proposed environment-economic planning two-level game model considering dynamic energy pricing strategies is verified using simulations. Because dynamic energy pricing and the environment-economic planning are considered, the number of energy equipment required during peak hours is reasonably reduced, thereby reducing the total planning cost and improving the energy utilization efficiency. Simultaneously, greenhouse gas (CO2) and air pollutant (NOx) emissions are reduced to decrease environmental impact.

Secure analysis of dynamic networks under pinning attacks against synchronization

In this paper, we consider a secure problem in dynamic networks. A malicious attacker may attack the pinning controlled nodes and prevent the synchronization in the network. The network defender needs to secure the nodes with limited protective budget and increase the difficulties for launching attacks, while the attacker needs to decide the target nodes to attack. A resource allocation model for the defender and the malicious attacker is developed. A leader–follower Stackelberg game framework is proposed to study the behavior of both sides and the equilibrium of this security game is investigated. Numerical examples and simulations are presented to illustrate the main results.

Secure and Efficient Vehicle-to-Grid Energy Trading in Cyber Physical Systems: Integration of Blockchain and Edge Computing

Smart grid has emerged as a successful application of cyber-physical systems in the energy sector. Among numerous key technologies of the smart grid, vehicle-to-grid (V2G) provides a promising solution to reduce the level of demand-supply mismatch by leveraging the bidirectional energy-trading capabilities of electric vehicles. In this paper, we propose a secure and efficient V2G energy trading framework by exploring blockchain, contract theory, and edge computing. First, we develop a consortium blockchain-based secure energy trading mechanism for V2G. Then, we consider the information asymmetry scenario, and propose an efficient incentive mechanism based on contract theory. The social welfare optimization problem falls into the category of difference of convex programming and is solved by using the iterative convex-concave procedure algorithm. Next, edge computing has been incorporated to improve the successful probability of block creation. The computational resource allocation problem is modeled as a two-stage: 1) Stackelberg leader-follower game and 2) the optimal strategies are obtained by using the backward induction approach. Finally, the performance of the proposed framework is validated via numerical results and theoretical analysis.

Jointly optimizing microgrid configuration and energy consumption scheduling of smart homes

Abstract In this paper, we formulate joint optimization of microgrid configuration and energy consumption scheduling as a leader-follower Stackelberg game to model the coordination between two rational decision makers of microgrid configuration and energy consumption scheduling. The microgrid configuration decision, as the leader, is modeled as an upper-level optimization problem for optimal installed numbers of wind turbines, photovoltaic (PV) units, micro-turbines and batteries. The energy consumption scheduling, as the follower, is modeled as a lower-level optimization problem, which responds to decisions of the upper level in order to determine the optimal appliance scheduling. A bi-level nonlinear programming model is formulated for the Stackelberg game. To solve this optimization model, four bi-level hierarchical algorithms with the combination of different evolutionary algorithms are implemented and compared. A case study of microgrid configuration of smart building is employed to demonstrate the feasibility and advantage of the proposed game-theoretic model.

Remanufacturing Models Under Technology Licensing with Consideration of Environmental Issues

Recently, the environmental and economic benefits of remanufacturing result in increasing interest of this concept. Due to supreme importance of this issue, in this paper, a closed-loop supply chain (CLSC) including a manufacturer, a distributor, and third-party logistics provider is considered. Three multi-level leader-follower Stackelberg game models are presented in order to investigate whether a manufacturer in addition to manufacturing new products should do remanufacturing or sets a fee for technology licensing of distributors and cooperate with them in remanufacturing. Furthermore, we conduct a sensitivity analysis to show how government can mitigate the bad economic, environmental, and social impacts of remanufacturing by setting an emissions tax price and evaluation of impacts of changing remanufacturing parameters on the profit of supply chain members on the three proposed models.

A Stackelberg Game-Theoretical Approach to Maritime Counter-Piracy

In this paper, we provide a maritime counter-piracy framework to represent the strategies put in place and the interaction between a set of actors (patrollers and attackers) in a wide maritime scenario. Specifically, we model the interaction between patrollers and attackers in terms of a Stackelberg leader-follower game. With respect to the previous literature, we provide several innovations, in that we consider moving targets. Moreover, we let the attackers and patrollers ground their decisions not only on the current situation, but also on the expected evolution in the short or medium term. This is done by introducing in the payoff functions some projection terms, i.e., elements able to consider the future evolution of the scenario, up to a specified time window horizon. We conclude this paper with a simulation campaign considering a realistic test bed settled in the Gulf of Aden. Our experiments show that such a prediction is quite effective in generating better decisions allowing the patrollers to dynamically change targets. However, if the time horizon considered in the projection term is too large, we observe that the patrollers tend to patrol the area rather than focusing on specific vessels, and the resulting protection strategy has reduced effectiveness.

Joint optimization using a leader–follower Stackelberg game for coordinated configuration of stochastic operational aircraft maintenance routing and maintenance staffing

Abstract The flight delay-based operational aircraft maintenance routing problem (OAMRPFD) and the maintenance staffing problem (MSP) are interrelated and interdependent. Despite this interdependency, each problem is solved separately. Therefore, the optimal plan specified by each problem is not executed as planned, which consequently increases the operating cost of each aspect of the problem. The present research paper studies OAMRPFD in addition to MSP, with two main objectives. The first is to develop an OAMRPFD model that appropriately reflects the flight delay and, accordingly, a new stochastic framework of a scenario-based OAMRPFD (SOAMRPFD) is put forward. The second is to handle the interdependence between SOAMRPFD and MSP, by proposing a coordinated configuration of SOAMRPFD and MSP that is formulated like the leader–follower Stackelberg game, with SOAMRPFD as the leader and MSP as the follower. A bi-level optimization model is used to present this game and is solved by a bi-level nested ant colony optimization (ACO) algorithm. The viability and potential of the proposed model are established using a major airline and a maintenance company, which are based in the Middle East, as a case study. The results demonstrate significant cost savings for both the airline and maintenance company.

A three-level framework for balancing the tradeoffs among the energy, water, and air-emission implications within the life-cycle shale gas supply chains

Two critical challenges, namely high water resources consumption and growing greenhouse gas (GHG) emissions, are encountered across the current shale gas supply chains. This study presents a three-level modeling framework for economic and environmental life-cycle optimization of the shale gas supply chains. Life cycle analysis (LCA) approach and Stackelberg leader-follower game are integrated into the optimization framework to account for a hierarchical structure.This hierarchical framework is capable of not only addressing the sequential decision-making problem raised by decision makers at different levels (e.g., the whole-system decision maker as a leader and the environment-development decision maker as a follower), but also developing multilevel cooperative control of water management and GHG-emission mitigation. An application to the Marcellus Shale is then given to demonstrate the capabilities of the developed three-level model. An improved leader-follower-interactive solution algorithm based on satisfactory degree is presented to tackle the computational challenge of the three-level program. The overall satisfaction solution is generated for satisfying the goals of different decision makers by compromising the trade-offs among energy, water, and air-emission implications. Optimal solutions with respect to well drilling schedule, shale gas production, freshwater supply, wastewater treatment, GHG emissions, and electricity generation would be obtained. These analyses are capable of helping decision makers adjust their tolerances to make informed decisions for the supply chains. Moreover, the decision making is not kept static but improved by repeatedly communicating with both different models and sensitivity analysis. Through the communications, the robustness and objectivity of the model solutions can further be enhanced.

Manufacturing Decisions and Government Subsidies for Electric Vehicles in China: A Maximal Social Welfare Perspective

In order to address challenges in the sustainable development of transportation, economy, and environment, governments of China and conventional automobile manufacturers are extremely concerned about the development of the electric vehicle (EV) manufacturing industry and market. However, owing to the limitations of EVs and the government economic policies on decreasing subsidies in China, many manufacturers are worried about entering the EV market. Given the low consumer preference for EVs, using a leader-follower Stackelberg game model, we investigate the impact of government a subsidy on the optimal production and pricing decisions of an auto manufacturer who could produce both EVs and conventional vehicles. We characterize whether/under what conditions the manufacturer’s decision to offer EV products under government subsidy, whilst increasing its profits (a win-win situation). On the policy side, we delineate how government a subsidy can be set to realize the inherent economic, environmental, and social benefits of EV production (the triple win of EV production). We further investigate the impact of EV manufacturing- and society-related factors on the balance among manufacturer profits, environmental impact and social welfare. This study also finds that the adoption of EVs is not bound to be beneficial for the environment.

Socially optimal deployment strategy and incentive policy for solar photovoltaic community microgrid: A case of China

Aiming to meet the increasingly diversified demand of electricity and abate emissions of electricity sector, the solar photovoltaic-powered community microgrid (SPCM) is encouraged in China. Based on an understanding of the distributed solar radiation intensity (SRI) in China, this paper explored the socially optimal deployment strategies of SPCM. And by formulating a leader–follower Stackelberg game, we investigated the role that emission permits trade policy can play in inducing the choice of SPCM. The empirical results show that not all the areas in China are suitable for the promotion of SPCM. And the social emissions concern (ε) has a big impact on the socially optimal deployment strategy of SPCM. Two factors determine whether the SPCM is inducible in a specific area: the located SRI and the incentive policy. And for a specific area, resident makes the choice based on whether the SPCM could be profitable. The results also demonstrate that a high price of CERs can achieve the effect of feed-in tariff policy in inducing SPCM, and emission permits trade policy as a market incentive mechanism can also internalize the external costs of CO2 emissions.

The impact of competitive advantage on the investment timing in Stackelberg leader–follower game

ABSTRACTThis short note clarifies how the Stackelberg leader’s competitive advantage after the follower’s entry affects the leader’s optimal market entry decision and Stackelberg strategic interactions under uncertainty. Although the Stackelberg leader’s first investment threshold remains constant and coincides with the monopolist’s investment trigger, his second (third) investment threshold, which defines the exit (entry) of the first (second) investment interval, increases with an increased competitive advantage. With an increased competitive advantage, the probability of sequential investment equilibrium (simultaneous investment equilibrium) increases (decreases) irrespective of the level of volatility. Moreover, for a given level of competitive advantage, an increase in the volatility tends to decrease (increase) the probability of simultaneous investment equilibrium (sequential investment equilibrium). For a richer set of results, endogenous firm roles are examined and analyzed as well. The leader’s preemptive threshold is negatively affected by his competitive advantage.

Energy-Efficient Localization Game for Wireless Sensor Networks

We study the energy saving problem of nodes for the hybrid directions of arrival/received signal strength (DoA/RSS) localization scheme in wireless sensor networks. To solve this problem, both the transmission power and the sleep times of the anchor nodes are allocated while the target is required to be localized with a pre-specified accuracy. We use the leader–follower Stackelberg game to model our problem, in which, the target is the follower and the set of the target’s neighbor anchor nodes, named coalition of anchor nodes (CANs), is the leader. We prove the existence and uniqueness of the Stackelberg equilibrium (SE) by giving closed-form expressions for the SE strategies of both the target and the CANs. The superior performance of the proposed scheme is validated through simulations.