Master-slave Game Research Articles

Two-Layer Game Theoretic Microgrid Capacity Optimization Considering Uncertainty of Renewable Energy

Configuration and operation are key to the successful deployment of a renewable energy integrated microgrid. Considering that wind generator, photovoltaic array, and storage battery may belong to different investors in market-oriented operation modes, game theory can be used to tackle the conflict between the overall optimal operation of the microgrid and the maximum profit of each investor. To handle the tradeoff among multiple investors and the uncertainties in wind and solar power, this article develops a new two-layer game model, where a planned output game and a capacity allocation game are considered. The inner layer is a master-slave game to optimize the planned renewable energy output, which is used to predetermine the operation strategy of the microgrid under the initial capacity allocation. In the outer layer, based on the optimized planned output obtained from the inner layer, a noncooperative game and a cooperative sequential game dominated by wind-photovoltaic cooperative alliance are formed to determine the optimal capacity allocations. The equilibrium solution, achieved from the iterative optimization between inner and outer layers, determines the optimal capacity allocation of the microgrid. The effectiveness of the proposed model is verified using a case study of a wind/photovoltaic/battery/gas microgrid.

Research on collaborative innovation among enterprises in green supply chain based on carbon emission trading.

Considering the multiple effects of product greenness and carbon emission trading, this article constructs a differential game model to study the collaborative innovation between enterprises in a green supply chain composed of one manufacturer and one supplier. This article examines the optimal green technology innovation strategies, optimal revenues of manufacturers and suppliers as well as the overall green supply chain revenues in the Nash non-cooperative game model, the Stackelberg master-slave game model, and cooperative game model, respectively. Through the comparative analysis of equilibrium results, it is found that the optimal strategies of suppliers and manufacturers as well as the total revenue of the green supply chain in the cooperative games are better than those in the non-cooperative game scenario. Meanwhile, undertaking part of suppliers' green innovation cost by manufacturers is the Pareto optimization mechanism that increases the total revenue of the green supply chain and their respective revenues. The research results of this article provide theoretical support for green supply chain enterprises to formulate incentive mechanisms for scientific strategy-making and reasonable revenue distribution.

Interactive Equilibrium of Electricity-Gas Energy Distribution System and Integrated Load Aggregators Considering Energy Pricings: A Master-Slave Approach

Integration of electricity and gas distribution networks improves energy utilization and alleviates environmental pollution. In order to obtain a reasonable energy prices and optimize the day-ahead scheduling scheme under the premise of considering the interests of both supply and demand, an interactive equilibrium model considering electricity-gas energy distribution system and integrated load aggregators is established in this paper. In the upper level, the integrated energy distribution network (IEDN) maximizes the profit via solving the day-ahead optimal energy flow considering energy prices changing in the next day. In the lower level, integrated load aggregators (ILA) minimize charging costs, thus optimizing energy distribution based on integrated demand responses. By using the Karush-Kuhn-Tucker (KKT) optimality conditions and the duality theorem of linear programming, the master-slave game model is transformed into a single layer optimization problem. To solve this problem, second-order cone programming (SOCP) and penalty convex-concave procedure (PCCP) are used to deal with the non-convex functions of electricity-gas distribution system. Therefore, the proposed model is approximated by a mixed-integer second-order cone programming problem. Finally, case studies verify the effectiveness of the proposed model and method.

A Differential Game-Based Approach for School-Enterprise Collaborative R&D Strategy on Digital Twin Technology

Digital twin (DT) technology is an effective way to realize intelligent manufacturing, which has been increasingly received attention in both academia and industry. Thus, it is rather necessary and significant to collaboratively accomplish the research and development (R&D) of DT technology (RDDT). To explore a school-enterprise collaborative R&D strategy on DT technology, this paper proposes a differential game-based approach to compute the optimal R&D effort levels and optimal incomes of both parties in the school-enterprise collaborative innovation (SECI) system. First, using Berman's continuous dynamic programming theory, the optimal R&D effort levels, the optimal incomes of both parties, and total optimal income in the SECI system are calculated in three cases: Nash non-cooperative game, Stackelberg master-slave game and cooperative game. Second, the equilibria of the three game cases are analyzed and compared. Finally, a numerical example is used to verify the validity of the conclusion, and we find that the optimal benefit of two parties in cooperative game are significantly better than those of Nash non-cooperative game and Stackelberg master-slave game, which effectively demonstrates the superiority of school-enterprise collaborative R&D on DT technology.

Analysis of Environmental Policy’s Impact on Remanufacturing Decision Under the Effect of Green Network Using Differential Game Model

Consumers' environmental protection awareness promotes the quality of green products produced by remanufacturers, which requires higher input cost and more efforts but wins environmental reputation in return. In order to encourage remanufacturers to produce products with less pollution, government enacts environmental policy to subsidy the production of remanufacturing. This paper aims to analyze the impact of subsidy on remanufacturing decision and identify the optimal decisions under the effect of green network using a differential game model. First, both government and remanufacturer's cost functions are established with their own environmental effort, respectively. Then, their benefit functions are built to represent their own reward, in which multiple factors are taken into account including but not limited to the environmental reputation of remanufacturer and consumers' demand for remanufactured products. Using the models of Nash-non cooperative game, Stackelberg master-slave game and cooperative game, their benefits are calculated and compared. The equilibrium results show that the improvement level of products' environmental quality is equal to the level of subsidies, and subsidies will increase with the improvement of products' environmental quality. In addition, with the support of the government, remanufactures are able to produce the most environmentally friendly products with the most benefit. Finally, a case study is given to prove the theorems obtained in this paper.

An Interactive Strategy of Grid and Electric Vehicles Based on Master-Slaves Game Model

In order to avoid the adverse effects of the grid caused by disorder large-scale electric vehicles and improve supporting function of energy storage battery on the power grid, interaction model of electric vehicles (EVs) and the power grid is constructed according to a master-slave game method. Then, the utility functions of each participant are established, and the dynamic constraints of the batteries for EVs are established considering the travel demand of users. Then, based on the YALMIP/CPLEX solver, the optimal response strategy of the EVs can be obtained, and the genetic algorithm is used to solve the Nash equilibrium solution of the master-slaves game model. Moreover, the Monte Carlo method is employed to simulate the user travel data and the basic parameters of EVs in a certain area. Based on these data, the optimal time-of-use price in this area is offered, and the optimal response strategy of EVs under this price is analyzed. Finally, the study of the case show that the proposed game model can make the strategies of both the EVs and the grid, which can restrict the load fluctuation of the grid and improve the benefit of EVs without affecting their travel.

Differential Game Analysis of Scientific Crowdsourcing on Knowledge Transfer

Scientific crowdsourcing based on knowledge transfer between enterprises has drawn wide attention. This paper constructs the Stackelberg master–slave game model and the benefit sharing model. Through the model comparison and numerical simulation, the knowledge transfer behavior and the revenue distribution mechanism of crowdsourcing initiator and solver in the context of scientific crowdsourcing are studied. The research shows that the knowledge transfer quality and the crowdsourcing total revenue under the benefit sharing state are better than the Stackelberg master–slave game under the leadership of the crowdsourcing initiator and when the revenue distribution coefficient between the crowdsourcing initiator and solver is within a certain range. The final revenue for each party in the benefit sharing state is higher than the one in the Stackelberg master–slave game state. In addition, the research finds that the knowledge coupling degree between the initiator and the solver has a positive impact on knowledge transfer and crowdsourcing benefits. The conclusions of this paper provide a theoretical basis for enterprises, especially for large-scale high-tech business to business enterprises, to transfer knowledge and distribute revenue and eventually improve their scientific crowdsourcing quality.

Study on Benefit Coordination of Supply Chain Network Based on Green Development.

Based on Stackelberg’s master–slave game theory and green index decision-making conditions, this paper studies the benefit coordination of a supply chain network composed of a business flow network and logistics network, discusses the decision-making behavior of the main body of the supply chain network under the performance of green contracts or speculative behavior, respectively, and further constructs the supply chain network collaborative benefit coordination model under the guidance of a manufacturer considering a green development index. The supply chain network interest coordination model analyzes the relationship between the dominant manufacturer behavior and the supply chain network green index and network profit. The results show that fulfilling green contracts helps improve the profitability and sustainability of supply chain networks. A counter-intuitive but interesting result is that the dominant manufacturers increase the cost-sharing ratio or penalties of the logistics network, which will reduce the profit level and green index of the logistics network, and increase the cost-sharing ratio or punishment of the suppliers. Strength will increase the profitability and green index of the logistics network. Finally, we validate the relevant conclusions of the model through numerical simulation analysis.

Does Urbanization Improve Industrial Water Consumption Efficiency?

Although some studies have focused on the logical connection between industrial water consumption in the industrial economic development (IED) and industrial wastewater treatment (IWT) stages, the master–slave game relationship between these stages has not been considered. This study selected panel data from 30 provinces in China from 2011 to 2015, divided these provinces into IED- and IWT-dominated regions, and developed a two-stage data envelopment analysis (DEA) model based on the master–slave game relationship between the IED and IWT stages. In addition, a regression model based on the Simar–Wilson approach was constructed to reveal the effects of urbanization on industrial water consumption efficiency. The results show that the industrial water consumption efficiency in China slightly fluctuated from 2011 to 2015, and there was no significant efficiency improvement. The efficiency of the IED stage was generally higher than that of the IWT stage, and the efficiency gap between stages was smaller in IED-dominated regions than in IWT-dominated regions. Urbanization has different effects on industrial water consumption efficiency, and the same factor can have significantly different effects in different regions. Some policy implications are proposed for the different types of regions.

Smart grid scheduling and control based on master–slave game

ABSTRACTElectric power dispatch is an effective management method used to ensure the safe and stable operation of the power grid, however, there will be some conflicts of interest between the power selling company and the power generation company during the dispatch process. This article aims to minimize the cost of electricity purchased by the power grid company and maximize the sales revenue of power generating company. In this paper, the decision-making space is based on the set of strategies for each power plant output and the on-grid price, proposing a master–slave game scheduling model in which the power grid company is used as the main game and power plants are the game followers. By using the cuckoo algorithm to optimize the master–slave game model, scheduling test results show that master–slave game scheduling provides better overall performance than economic dispatch.

Influence of government regulation on the stability of dual-channel recycling model based on customer expectation

In this paper, the consumers choose different channels to take part in recycling based on the utility they get. A recovery master–slave game model based on customer utility expectations which includes online recyclers, offline recyclers and remanufacturers is established, and the game process which consists of two links which adopt heterogeneous decision-making methods is discussed. And further, a dynamic intervene method which the government subsidizes for maximizing social welfare is considered. This paper analyzes the source of system instability in each link and the impact of relevant parameters on system stability and profitability. The impact of government intervention on system stability is also studied. The results show that chaos occurs with the increase in the remanufacturer’s sensitivity. But with the government’s emphasis on environmental protection within a reasonable range, the chaos can be controlled and the system’s profits rise.

A stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises under uncertain environment

Abstract Considering the fact that the development of low carbon economy calls for the low carbon technology sharing between interested enterprises, this paper study a stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises. In the paper, we consider the random interference factors that include the uncertain external environment and the internal understanding limitations of decision maker. In the model, superior enterprises and inferior enterprises are separated entities, and they play Stacklberg master-slave game, Nash non-cooperative game, and cooperative game, respectively. We discuss the feedback equilibrium strategies of superior enterprises and inferior enterprises, and it is found that some random interference factors in sharing system can make the variance of improvement degree of low carbon technology level in the cooperation game higher than the variance in the Stackelberg game, and the result of Stackelberg game is similar to the result of Nash game. Additionally, a government subsidy incentive and a special subsidy that inferior enterprises give to superior enterprises are proposed.

Transferring green building technologies from academic research institutes to building enterprises in the development of urban green building: A stochastic differential game approach

This paper presents a stochastic differential game of green building technologies (GBTs) transfer from academic research institutes to building enterprises in the building enterprises-academic research institutes collaborative innovation (BACI) system. Some random interference factors, for example the uncertain external environment and the mood of decision makers, are considered into three models which are Nash non-cooperative game model, Stacklberg master-slave game model and cooperative game model. The equilibrium strategies of building enterprises and academic research institutes are studied and discussed by using feedback control. The equilibrium results showed that the effort level of academic research institutes and building enterprises is proportional to the government subsidy of GBTs innovation, and the level of credit support and tax relief is proportional to the effort level of academic research institutes. The government subsidy of GBTs innovation is a long-term incentive mechanism which can promote GBTs transfer from academic research institutes to building enterprises in the BACI system. The Pareto optimality of GBTs transfer system can be reached under a cooperative game model. To reach the Pareto optimality, the scope of revenue distribution coefficient is given by analysis of revenue distribution mechanism. This study will contribute to the GBTs transfer from academic research institutes to building enterprises by providing some incentive mechanisms and the scope of revenue distribution coefficient. The findings from this study also adds to theoretical basis of incentive mechanisms, random factors, profit distribution and contract design for building enterprises and academic research institutes to make scientific decisions.

Game-Theoretic Optimization of Bilateral Contract Transaction for Generation Companies and Large Consumers with Incomplete Information

Bilateral contract transaction among generation companies and large consumers is attracting much attention in the electricity market. A large consumer can purchase energy from generation companies directly under a bilateral contract, which can guarantee the economic interests of both sides. However, in pursuit of more profit, the competitions in the transaction exist not only between the company side and the consumer side, but also among generation companies. In order to maximize its profit, each company needs to optimize bidding price to attract large consumers. In this paper, a master–slave game is proposed to describe the competitions among generation companies and large consumers. Furthermore, a Bayesian game approach is formulated to describe the competitions among generation companies considering the incomplete information. In the model, the goal of each company is to determine the optimal bidding price with Bayesian game; and based on the bidding price provided by companies and the predicted spot price, large consumers decide their personnel purchase strategy to minimize their cost. Simulation results show that each participant in the transaction can benefit from the proposed game.

Study on Complex Advertising and Price Competition Dual-Channel Supply Chain Models Considering the Overconfidence Manufacturer

In order to explore how the manufacturers make decisions when two manufacturers compete for local advertising investment, we examine two noncooperative models (Stackelberg and Nash game) and propose a cost sharing contract to investigate channel competition of dual-channel supply chain. The dominant power between manufacturer and retailer and the effect of channel competition strategy on price are mainly discussed. In addition, dynamic system concepts are integrated into Stackelberg game model based on bounded rational mechanism. We analyze the local stability and find that the stability level of the dual-channel supply chains depends crucially on the price adjustment speed, the level of demand uncertainty, and the risk preference. The outcome shows that, under the master-slave game model, the profits of manufacturers are greater than that under decentralized decision-making mode, and the profits of retailers under master-slave game model are less than that under decentralized decision-making mode. The profits of manufacturers and retailers in the stable region are greater than that in unstable region. Finally, the delay feedback control method is utilized and effectively controls the chaotic behavior of dual-channel supply chain model. The results have theoretical and practical significance for the game models in terms of advertising and price competition.

Complexity Analysis of a Master-Slave Oligopoly Model and Chaos Control

We establish a master-slave oligopoly game model with an upstream monopoly whose output is considered and two downstream oligopolies whose prices are considered. The existence and the local stable region of the Nash equilibrium point are investigated. The complex dynamic properties, such as bifurcation and chaos, are analyzed using bifurcation diagrams, the largest Lyapunov exponent diagrams, and the strange attractor graph. We further analyze the long-run average profit of the three firms and find that they are all optimal in the stable region. In addition, delay feedback control method and limiter control method are used in nondelayed model to control chaos. Furthermore, a delayed master-slave oligopoly game model is considered, and the three firms’ profit in various conditions is analyzed. We find that suitable delayed parameters are important for eliminating chaos and maximizing the profit of the players.