Two-stage Dynamic Game Model Research Articles

Does cooperative intervention affect pricing decisions in the agricultural supply chain?

In global agricultural markets, farmers often face profit squeezes due to low bargaining power, which affects the sustainability of agriculture and the livelihoods of farmers. Cooperative intervention is seen as a key solution to improve bargaining power and optimize profit distribution in the agricultural supply chain. In this study, a two-stage dynamic game model is adopted to focus on bargaining power and compare the effects of linear pricing versus a double charging system under cooperative intervention. It is found that the cooperative is better when it has full bargaining power or when it faces downstream sellers with comparable bargaining power, and the dual-charging system is more favorable. When cooperatives bargain with sellers, the degree of differentiation of agricultural products affects the cooperatives’ profitability and cooperatives tend to maintain the two-part tariff when the bargaining power is less than a threshold condition containing the degree of differentiation of agricultural products; when discounts exceed the threshold, cooperatives shift to linear pricing to safeguard their profitability. Numerical analysis validates the theory and reveals the changing pattern of cooperative profits under market forces. This study not only provides theoretical support for the study of supply chain pricing strategies under the condition of considering the bargaining power of producers (farmers) but also provides management insights for the stability and sustainable development of agricultural supply chains. Its novel dynamic game framework is cross-culturally applicable to help farmers’ cooperatives cope with the challenge of profit distribution in a global context and emphasizes the importance of differentiation strategies to enhance bargaining power and promote fairness and efficiency in global agricultural supply chains.

Equilibrium Interaction Strategies for Integrated Energy System Incorporating Demand-Side Management Based on Stackelberg Game Approach

This paper analyzes the balanced interaction strategy of an integrated energy system (IES) operator and an industrial user in the operation process of the IES under the demand-side management (DSM) based on game theory. Firstly, we establish an electric–thermal IES, which includes a power grid, a heat grid and a natural gas grid. Secondly, a two-stage Stackelberg dynamic game model is proposed to describe the game behavior of IES operators and industrial users in the process of participating in DSM. The interactions between the IES operator (leader) and the user (follower) are formulated into a one-leader–one-follower Stackelberg game, where optimization problems are formed for each player to help select the optimal strategy. A pricing function is adopted for regulating time-of-use (TOU), which acts as a coordinator, inducing users to join the game. Then, for the complex two-stage dynamic game model established, the lower user-side constraint optimization problem is replaced by its KKT condition, so that the two-stage hierarchical optimization problem is transformed into a single-stage mixed-integer nonlinear optimization model, and the branch-and-bound method is introduced to solve it. Finally, the equilibrium strategies and income values of both sides of the game are obtained through a case simulation, and the dynamic equilibrium strategy curves under different capacity configurations are obtained through the sensitivity analysis of key parameters. The equilibrium income of the IES is USD 93.859, while the equilibrium income of industrial users in the park is USD 92.720. The simulation results show that the proposed method and model are effective.

Economic optimization scheduling of virtual power plants considering an incentive based tiered carbon price

Against the backdrop of China's carbon peak and carbon neutrality goals, the use of virtual power plants for electricity economic dispatch has gradually become a research hotspot. The virtual power plant includes both supply and demand sides. If the inherent conflicts of interest between both parties cannot be effectively addressed, there are significant hidden dangers in the sustainable operation of the virtual power plant. On the basis of existing research, this article constructs a regional virtual power plant. With the goal of maximizing supply and demand utility, a two-stage Stackelberg dynamic game model was established between virtual power plant operators and users in the electricity market and carbon trading market mechanisms, and an incentive based hierarchical carbon price constraint was designed in the optimization model. In the model constructed in this article, the operator of a virtual power plant will consider environmental benefits based on expected returns, adjust the output of controllable units to change the electricity supply strategy, and formulate a pricing strategy. At the same time, users will adjust their electricity consumption strategy based on their own electricity consumption characteristics, and both will achieve a game equilibrium. Based on the optimization results, this article conducted a sensitivity analysis on the incentive coefficient of graded carbon prices and obtained the optimal incentive coefficient under the case conditions. The research results indicate that the model can coordinate and meet the interests and needs of both the power generation and consumption sides, and the implementation of incentive based hierarchical carbon pricing strategies has certain advantages compared to traditional carbon pricing strategies in different user types scenarios. The research conclusion of this article has good reference value for the sustainable green operation of virtual power plants.

Optimal government subsidy strategy for fresh agricultural products supply chain under adverse weather: a two-stage dynamic game model

ABSTRACT To investigate the effects of various government subsidies on the decision of agricultural products supply chain under adverse weather, this paper depicts the random profit function of adverse weather affecting the output of fresh agricultural products. Then, both the centralised and decentralised decision-making models are set with various government subsidies, i.e. no subsidy, output subsidy, procurement subsidy, one-time subsidy to company and one-time subsidy to farmer. Through comparative analysis and numerical analysis, we explore the effects of adverse weather and different government subsidies on the supply chain decisions including planting effort, procurement price and retail price.

Optimal defense strategy for AC/DC hybrid power grid cascading failures based on game theory and deep reinforcement learning

This paper proposes a two-person multi-stage zero-sum game model considering the confrontation between cascading failures and control strategies in an AC/DC hybrid system to solve the blocking problem of DC systems caused by successive failures at the receiving end of an AC/DC system. A game model is established between an attacker (power grid failure) and a defender (dispatch side). From the attacker’s perspective, this study mainly investigates the problem of system line failures caused by AC or DC blockages. From the perspective of dispatch-side defense, the multiple-feed short-circuit ratio constraint method, output adjustment measures of the energy storage system, sensitivity control, and distance third-segment protection adjustment are used as strategies to reduce system losses. Using as many line return data as possible as samples, the deep Q-network (DQN), a deep reinforcement learning algorithm, is used to obtain the Nash equilibrium of the game model. The corresponding optimal dispatch and defense strategies are also obtained while obtaining the optimal sequence of tripping failures for AC/DC hybrid system cascading failures. Using the improved IEEE 39-node system as an example, the simulation results verify the appropriateness of the two-stage dynamic zero-sum game model to schedule online defense strategies and the effectiveness and superiority of the energy storage system participating in defense adjustment.

Risk Dominance Analysis of R&D Investment Cooperation in Dynamic Option Game

Research and development (R&D) investment is very important for firms to gain competitive advantages and sustainable development. Due to the uncertainty of the market and competitors, R&D investment is usually costly and high risk. In such circumstances, firms not only have to figure out the optimal investment timing, but also consider whether to cooperate with competitors to share the risks and costs. In this paper, a two-stage dynamic exchange option game model is proposed for two symmetric competing firms to analyze their R&D investment decision and cooperation. The results show that under uncertainty, the R&D investment timing and cooperation strategy of the two firms depend on the market fluctuation, R&D cost, opportunity benefit of free riding, and the externality of cooperation. If the opportunity benefit of free riding is less than or equal to half of the cooperative research cost, the two firms will invest as early as possible and cooperate. The technology spillover and profits of new products will positively affect the willingness of the competing firms to invest and cooperate in R&D. Moreover, we also calculate the market value thresholds of the investment strategies for the two firms. When the market value is small, the two firms wait for the R&D investment; when the value increases, the firm with a high successful R&D probability will lead the investment, and the other firm follows the investment; when the value is large enough, the two firms will invest at the beginning of the period.

Dynamic Pricing Strategy for Two-Generation Products under Different Trade-in Subsidy Strategies

Trade-in is one of the most widely used recycling methods in practice. A key problem in the trade-in process is the dynamic pricing strategy under different trade-in subsidy strategies. Consumers are divided into myopic and strategic consumers. Considering three situations, namely, (1) no trade-in subsidy strategy, (2) the firm’s trade-in subsidy strategy, and (3) the government’s trade-in subsidy strategy, the dynamic game equilibrium between firms and consumers is analyzed. The optimal dynamic pricing strategy is obtained by constructing a two-stage dynamic game model. The results show that (1) the number of consumers who purchase next-generation new products is not impacted by the trade-in subsidy strategy. However, the number of consumers who engage in trade-ins is impacted by the trade-in subsidy strategy. (2) The number of consumers who engage in trade-ins with the trade-in subsidy strategy is larger than that without the trade-in subsidy strategy. (3) Compared with the government’s trade-in subsidy strategy, the firm’s trade-in subsidy strategy can more effectively motivate consumers to engage in trade-in activity.

Reflection on the joint prevention and control of air pollution from the perspective of environmental justice-insights from a two-stage dynamic game model.

The practices of the joint prevention and control of air pollution (JPCAP) present two disadvantages: the low enthusiasm of governance subjects and an unsatisfactory governance effect. Revealing the existing problems and exploring their causes has been a key issue for promoting JPCAP. Given this, we especially establish a two-stage dynamic game model for air pollution control to explore the advantages and dilemmas of JPCAP by analyzing changes in environmental tax rate and social welfare. The results show that the unfair distribution of social welfare among cities is a key reason for the unsatisfactory effect of JPCAP. Therefore, we improve JPCAP by considering both production-oriented and consumption-oriented pollutions based on environmental justice. In the improved JPCAP mode, the social welfare of each city is higher than that of non-joint control of air pollution (NJCAP), in which the increased degree is positively related to the city's negotiation ability. In addition, the consumption tax rate is negatively correlated with the negotiation ability of the central city and the trade transfer coefficient. This study not only provides a theoretical and methodological reference for formulating effective planning and compensation scheme for JPCAP but also can be extended to the practice and theoretical analysis of other cross-regional public issues.

Research on the influence of product differentiation and emission reduction policy on CO2emissions of China’s iron and steel industry

PurposeThere are certain differences in the production products of enterprises. What are the impacts of product differentiation on the iron and steel industry? Based on the macro background of CO2emission reduction, this paper aims to analyze the economic benefits and environmental changes of the iron and steel industry under the dual influence of CO2emission reduction policy and product differentiation policy.Design/methodology/approachTaking the basic data of iron and steel industry in six regions of China as an example, this paper constructed an extended two-stage dynamic game model to analyze the impact of product differentiation and carbon tax policy on the production, economic indicators and CO2emission levels for the overall industry and regional enterprises.FindingsAs the CO2emission reduction target increased, the unit carbon tax and total tax increased, whereas the macro-environmental losses, social welfare, consumer surplus and outputs decrease. Emission reduction pressures and other economic indicators showed obvious regional differences. Differentiated products promoted various indicators of enterprises and industries; higher degrees of product differentiation resulted in greater promoting effects on economic indicators.Originality/valueThis paper constructed multiple emission reduction and production backgrounds, and discusses the impact of the comprehensive implementation of these policies, which has been practically absent in previous studies. The results of this study are consistent with the current industrial policy for stable production and environmental protection, and also provides a reference for the formulation of detailed policies in the future.

Pricing strategy of cloud monitoring platform based on bilevel stochastic programming

Pricing is a key decision of enterprise operation. As a new industry, the cloud service has not yet formed a unified pricing standard. Aiming at the pricing problem of cloud monitoring service platform, this paper analyzes the interest relationship between providers of cloud monitoring service and customers, establishes a two-stage dynamic game model, and extracts the core parameters and variables for the target of profit maximization. This paper also takes into account the uncertainty of equipment failure and production loss, and constructs a bilevel stochastic programming model, then a new algorithm combined with pole search method is proposed to find the global optinal solution. Finally, an example is given to demonstrate the model effectiveness. The computation results show that the profit of the provider is increasing with the increase of the number of customers. At the same time, the multi-type service mode will help the service provider increase its profit to a certain extent. By adjusting the pricing strategy, the platform makes most customers purchase the basic service type and the remaining customers choose the deep service, often optimizes the profits of service providers.

Research on the Influence of Bounded Rationality and Product Differentiation on the Stability of Steel Industry Market

At present, the problems of homogenization and low quality in China’s iron and steel industry are particularly prominent and the ability of the enterprises to cope with change is insufficient. Adopting product differentiation strategy and dynamic adjustment strategy can allow steel enterprises and the industry to better adapt to future changes. By introducing the product differentiation degree (substitution coefficient) and the bounded rationality strategy to simulate these two strategic means, this paper constructs an extended two-stage dynamic game model to analyse the dynamic game scenarios and steel market stability in China. As new findings, we report the following: (1) The system is more likely to fall into an unbalanced state when multiple enterprises adopt the policy of dynamic output adjustment simultaneously. (2) Enterprises with large output and small output have different output adjustment policies. When enterprises with big-scale output adopt a bit larger adjustment policies, enterprises with small output will be strongly impacted, and the available adjustment space will be sharply compressed. (3) The gradual increase in the difference between products reduces the stability of the market. (4) When product differentiation and bounded rationality strategies coexist, the steel market may fall into an unbalanced state when the degree of product difference increases excessively and the enterprise adopts more drastic output adjustment policies. Therefore, there are pros and cons to product differentiation strategy and bounded rationality adjustment strategy. When each steel oligopoly enterprise formulates a production plan, it needs to comprehensively consider the output changes of the other enterprises and carefully weigh the strategic issues.

Early bird or versioning

PurposeCrowdfunding, especially reward-based crowdfunding, has quickly evolved into a commonly used vehicle for innovating entrepreneurs to develop their products. Many crowdfunding platforms allow creators maximum flexibility in terms of the prices and rewards offered in a project to gain sufficient capital. However, creators need to understand how to design project rewards and how to select a pricing strategy, in addition to whether the creator should spend resources on designing multiple rewards of varying quality. The purpose of this paper is to address these issues by answering whether and why there are significant differences in the application of early-bird and versioning pricing strategies in crowdfunding.Design/methodology/approachThis paper develops a two-stage dynamic game model with incomplete information, proposes a corollary calculated by analyzing a perfect Bayesian equilibrium, and then tests Corollary 1 by empirical analysis.FindingsContrary to the findings of other studies, the results show that an early-bird pricing strategy is likely better than a versioning pricing strategy for earning greater revenue in a crowdfunding context, on average. This finding means that creators do not have to spend as much in designing rewards of various qualities; rather, they should only provide multiple price options for high-quality rewards. However, if the heterogeneity of target backers’ valuations and the quality difference between two types of products are adequately high, a versioning pricing strategy may be a good choice for creators.Practical implicationsThis paper provides a reference for creators regarding the selection of pricing strategies and the design of reward quality when launching crowdfunding projects.Originality/valueThis paper explains an interesting and practical issue in the design of reward quality and the selection of a pricing strategy after fully considering the role of the crowdfunding all-or-nothing mechanism and special backer behavior.

Improving Spectrum Management for Satellite Communication Systems With Hunger Marketing

Efficient spectrum management is an important issue in satellite communications due to the pervasive growth in wireless communications and the ever-increasing demand by bandwidth-hungry mobile applications. While various kinds of static and dynamic spectrum allocation schemes have been studied by satellite researchers, the issue of unpredictable user behavior, hence demand for bandwidth, remains one of the key challenges faced by the research community. In this letter, we introduce the hunger marketing strategy in satellite spectrum management in order to address the unpredictable user demands. When adopting hunger marketing, the system always maintain a certain level of spectrum supply shortage, thus stimulating the desire of users to plan and commit their bandwidth requirements in advance, hence making their behavior more predictable and benefiting satellite systems. Besides, in circumstances of multibeam satellite systems, when allocating bands to new satellite users, the issue of increase in inter-cell interference is also considered in this letter. Thus, a two-stage dynamic game model based on hunger marketing is proposed which aims to achieve an optimal balance between spectrum utilization and inter-cell interference. Numerical results are presented to show the effectiveness of the proposed method.

Research on the Impact of Various Emission Reduction Policies on China’s Iron and Steel Industry Production and Economic Level under the Carbon Trading Mechanism

To study the emission reduction policies’ impact on the production and economic level of the steel industry, this paper constructs a two-stage dynamic game model and analyzes various emission reduction policies’ impact on the steel industry and enterprises. New results are observed in the study: (1) With the increasing emission reduction target (15%–30%) and carbon quota trading price (12.65–137.59 Yuan), social welfare and producer surplus show an increasing trend and emission macro losses show a decreasing trend. (2) Enterprises’ reduction ranges in northwestern and southwestern regions are much higher than that of the other regions; the northeastern enterprise has the smallest reductions range. (3) When the market is balanced (0.8543–0.9320 billion tons), the steel output has decreased and the polarization in various regions has been alleviated to some extent. The model is the abstraction and assumption of reality, which makes the results have some deviations. However, these will provide references to formulate reasonable emissions reduction and production targets. In addition, the government needs to consider the whole and regional balance and carbon trading benchmark value when deciding the implementation of a single or mixed policy. Future research will be more closely linked to national policies and gradually extended to other high-energy industries.

Decisions of Green Supply Chain under Fairness Concerns and Different Power Structures

This article constructs a two-stage dynamic game model for green manufacturers, retailers, and consumers to address the issue that fairness preference in manufacturing can impact supply chain decision-making. This is done by discussing decision-making under the three power structures of green-manufacturer-dominated, retailer-dominated, and the Nash-equilibrium, and compares the balanced decision under the three power structures. The results show that in the manufacturer-dominated and Nash equilibrium games, product greenness, retailer profits, manufacturer profits, total supply chain profits, and a manufacturer's utility all decrease as the fairness preference increases, whereas the retail price and wholesale price are just the opposite of each other. In the retailer-dominated game, the retail price, product greenness, and total supply chain profits are not impacted by the fairness preference. The wholesale price, manufacturer's profits, and manufacturer's utility increases as the fairness preference increases, whereas the retailer profits decrease.

The Impacts of Regulations and Financial Development on the Operations of Supply Chains with Greenhouse Gas Emissions.

To establish a micro foundation to understand the impacts of greenhouse gas (GHG) emission regulations and financial development levels on firms’ GHG emissions, we build a two-stage dynamic game model to incorporate GHG emission regulations (in terms of an emission tax) and financial development (represented by the corresponding financing cost) into a two-echelon supply chain. With the subgame perfect equilibrium, we identify the conditions to determine whether an emission regulatory policy and/or financial development can affect GHG emissions in the supply chain. We also reveal the impacts of the strictness of GHG emission regulation, the financial development level, and the unit GHG emission rate on the operations of the supply chain and the corresponding profitability implications. Managerial insights are also discussed.

Research on CO2 Emission Reduction Mechanism of China’s Iron and Steel Industry under Various Emission Reduction Policies

In this paper, a two-stage dynamic game model of China’s iron and steel industry is constructed. Carbon tax levy, product subsidy, carbon capture and sequestration (CCS) and other factors are included in the emission reduction mechanism. The effects of emissions reduction and the economic impact of China’s overall steel industry (and that of its six main regions) are investigated for the first time under different scenarios. As new findings, we report the following: (1) Not all factors declined. The overall social welfare, consumer surplus, output and emissions decrease with a gradual increase in the reduction target, whereas the carbon tax value, unit value of product subsidies and total subsidies show a rising trend; (2) A combination of multiple emissions reduction policies is more effective than a single policy. With the implementation of a combined policy, regional output polarization has eased; (3) Steel output does not exceed 950 million tons, far below the current peak. These results will help the industry to formulate reasonable emissions reduction and output targets. In short, in effort to eliminate industry poverty and to alleviate overcapacity, the industry should not only adopt the various coordinated reduction policies, but also fully consider regional differences and reduction needs.

Credit Constraints and the Quality of Export Commodities in modern China: Taking Sino-foreign Tea Trade as an Example

In recent years, the increase in the quality of export commodities has become the urgent needs to improve the competitiveness of China's foreign trade. This paper starts on the analysis of the relationship among market participants in tea trade, explores the key barriers to the quality of tea export in modern China, and then builds a two-stage dynamic game model to analyze the effect of Ch'a Chans as the trade and financial intermediaries on the tea quality improvement. It finds that Ch'a Chans are the determinant affecting the quality of tea export in modern China, but the conflict between the private interests of Ch'a Chans and the tea quality improvement has become one of the main obstacles. The reasons basically lie in that it is difficult to form a long-run cooperation relationship between Ch'a Chans and tea manufacturers, thereby leading to the obtainment of only short-term loans from Ch'a Chans by tea manufacturers to ensure the supply of tea quantity and a lack of long-term loans to improve the quality of tea export. Furthermore, it conducts a more comprehensive historical analysis of reasons for the poor quality of Chinese tea export in modern times, and argues that the quality of tea export is subject to tea manufacturers'lack of incentives to improve the tea quality, and is hampered by multi credit constraints between intermediaries and financial system. In addition, a lack of the provision of powerful industry and fiscal policies in the late Qing Dynasty is also a restriction factor. The conclusions provide some enlightenment to the transformation of current China's foreign trade from quantity to quality and the enhancement of the supply-front reform to some extent.

Asymmetric competition in food industry with product substitutability

The paper analyses the effects of asymmetric competition on food industry with product substitutability by establishing a two-stage dynamic game model. The equilibrium is captured under both the Cournot competition and Stackelberg competition. Firstly, under the Cournot competition, lower costs yield a higher quality, more outputs and higher profits. Secondly, the cost difference increases the quality difference, the market size difference and the profit difference. Thirdly, a U-shaped relationship between the product substitutability and the food quality exists. Finally, compared with the case under the Cournot competition, the food security is significantly reduced with the lower quality and less outputs in the case under the Stackelberg competition.

Coopetition in Intermodal Freight Transport Services

The paper studies the coopetition of the downstream different carriers by providing complementary transport services in intermodal freight transport chain. Considering different information structure, a two-stage dynamic game model with simultaneous actions on investment and price is first formulated. Equilibria show both parties have motivation to select coopetition even if the agreement for cooperation investment is reached in advance. When both firms agree on the specific allocation, the new coopetition with higher efficiency would be emerged. Moreover, we analyze the complexity and evolution of coopetition by repeated pricing game with finitely and infinitely time horizon. In the finitely repeated pricing game, both firms have incentive to reach a tacit understanding to alternate choosing price cooperation and competition after setting suitable allocation scheme; the repeated periodstare then going to be an issue. In the infinitely repeated pricing game, the perfect cooperation is realized by designing the suitable trigger strategy.