Dynamic Game Research Articles

An analysis of optimal equilibrium in the carbon trading market - From a tripartite evolutionary game perspective

As the climate crisis intensifies, achieving the global consensus of carbon peaking and carbon neutrality has become imperative. Carbon trading is an important financial measure to address the environmental crisis, and the realization of the dual‑carbon goals requires the cooperation and joint efforts of all parties involved in the carbon emissions trading market. This study constructs a dynamic evolutionary game model involving enterprises, government, and financial institutions while considering consumers' influence. By solving for equilibrium points and conducting numerical simulations, we explore optimal strategy choices for each stakeholder. Our findings reveal that the success of enterprise low-carbon transition is contingent upon market dynamics and requires active cooperation from government, financial institutions, and the public. Furthermore, factors such as financial market efficiency and internal governance capacity significantly impact enterprises' transformation decisions by influencing low-carbon transition costs. Public feedback indirectly affects enterprise decisions through its influence on financial institutions' provision of green services. Additionally, gradual reduction of carbon quotas by government entities facilitates progress toward low-carbon transformation objectives.

Tripartite evolutionary game analysis of government reward and punishment mechanisms and agricultural resilience under a dual carbon context

PurposeUnder the “dual carbon” framework, the article explores the equilibrium points among the government, agricultural enterprises and village committees, and uses sensitivity analysis to reveal the dynamic factors affecting these stakeholders, thereby proposing methods to enhance agricultural disaster resilience.Design/methodology/approachThe article uses MATLAB to construct a game model for the three parties with interests: agribusiness, government and village council. It examines the stability of strategies among these entities. Through graphical simulation, the paper analyzes the sensitivity of agricultural enterprises carbon emissions and village committees’ rent-seeking behaviors in the decision-making process, focusing on significant factors such as government carbon tax and regulatory policies.FindingsA single government reward and punishment mechanism is insufficient to influence the strategic choices of enterprises and village committees. The cost of rent-seeking does not affect the strategic choices of enterprises and village committees. A key factor influencing whether the village committee engages in rent-seeking is the level of labor income of the village committee as an “intermediary”.Originality/valueThis paper focuses on the dynamic game between three stakeholders (the government, agricultural enterprises and village committees), seeking dynamic equilibrium and conducting sensitivity analysis through visualization to provide the government with optimal policy recommendations.

Agent-based evolutionary game dynamics uncover the dual role of resource heterogeneity in the evolution of cooperation

Cooperation is a cornerstone of social harmony and group success. Environmental feedbacks that provide information about resource availability play a crucial role in encouraging cooperation. Previous work indicates that the impact of resource heterogeneity on cooperation depends on the incentive to act in self-interest presented by a situation, demonstrating its potential to both hinder and facilitate cooperation. However, little is known about the underlying evolutionary drivers behind this phenomenon. Leveraging agent-based modeling and game theory, we explore how differences in resource availability across environments influence the evolution of cooperation. Our results show that resource variation hinders cooperation when resources are slowly replenished but supports cooperation when resources are more readily available. Furthermore, simulations in different scenarios suggest that discerning the rate of natural selection acts on strategies under distinct evolutionary dynamics is instrumental in elucidating the intricate nexus between resource variability and cooperation. When evolutionary forces are strong, resource heterogeneity tends to work against cooperation, yet relaxed selection conditions enable it to facilitate cooperation. Inspired by these findings, we also propose a potential application in improving the performance of artificial intelligence systems through policy optimization in multi-agent reinforcement learning. These explorations promise a novel perspective in understanding the evolution of social organisms and the impact of different interactions on the function of natural systems.

Blockchain Technology Adoption by Critical Stakeholders in Prefabricated Construction Supply Chain Based on Evolutionary Game and System Dynamics

Blockchain technology (BT) is a promising solution to address information asymmetry and trust issues in the prefabricated construction supply chain (PCSC). However, its practical application in PCSC remains limited under the influence of stakeholders’ adoption strategies. While previous studies have analyzed drivers and barriers to BT adoption, they often take a static view, neglecting the long-term dynamic decision-making interactions between stakeholders. This study addresses this gap by examining the interests of owners, general contractors, and subcontractors, and by developing a tripartite evolutionary game model to analyze the interaction mechanism of the strategy of adopting BT in PCSC. Additionally, a system dynamics simulation validates the evolution of stabilization strategies and examines the impact of key parameters. The results indicate that successful BT adoption requires technology maturity to surpass a threshold between 0.5 and 0.7, along with a fair revenue and cost-sharing coefficient between general contractors and subcontractors, ranging from 0.3 to 0.5 at the lower limit and 0.7 to 0.9 at the upper limit. Notably, general contractors play a pivotal role in driving BT adoption, acting as potential leaders. Furthermore, appropriate incentives, default compensation, and government subsidies can promote optimal adoption strategies, although overly high incentives may reduce owners’ willingness to mandate BT adoption. This study provides practical insights and policy recommendations for critical stakeholders to facilitate the widespread adoption of BT in PCSC.

Dynamic control of ecological restoration in abandoned mines under the background of ecology-oriented development in China

PurposeThis study examines how local governments and enterprises can implement ecological restoration of abandoned mines based on ecology-oriented development (EOD), which will be more beneficial to local environmental protection and economic development under the central government’s policy of outcome incentives or process subsidies.Design/methodology/approachWe construct a dynamic differential game model to simulate the interactions between local governments and enterprises during the ecological restoration of abandoned mines from an EOD perspective.FindingsThe findings suggest that under the central government’s outcome incentive policy, cooperation between local governments and enterprises is an optimal strategy. Under the process subsidy policy, while neither cooperative nor non-cooperative models significantly affect the investment levels of local governments and enterprises, a cooperative approach ensures optimal investments from both without solely relying on the process subsidy. Additionally, incorporating altruistic preferences can lead to Pareto improvements in economic and environmental results under central government outcome incentives.Practical implicationsThis research offers a policy foundation for governments to encourage the EOD model in the ecological restoration of abandoned mines. It provides theoretical support for achieving environmental sustainability and high-quality economic development, and is particularly significant for resource-depleted cities seeking to transform their development strategies.Originality/valueThrough a dynamic differential game model involving government agencies and enterprises to simulate decision-making in the ecological restoration of abandoned mines, incorporating altruistic preferences into this restoration process, and identifying optimal strategies and policies for ecological restoration.

Existence of equilibrium in a dynamic supply chain game with vertical coordination, horizontal competition, and complementary goods

We consider supply chain competition and vertical coordination in a linear–quadratic differential game setting. In this setting, supply chains produce complementary goods and each of them includes a single manufacturer and a single retailer who coordinate their decisions through a revenue-sharing contract with a wholesale price and a fixed sales revenue share. We study a multiple leader-follower Stackelberg game where the manufacturers are the leaders and the retailers are the followers. Competition occurs at both levels of the supply chains. Retailers play Nash and compete in price; manufacturers also play Nash but they compete in choosing their production capacities by exploiting the equilibrium price decisions made by the retailers. We show that open-loop Nash equilibria exist when the manufacturers only receive a wholesale price (there are no longer exploiting the equilibrium price decision made by the retailers, however). When the manufacturers receive both a wholesale-price and a share of the retailers’ sales revenues, equilibria generally no longer exist. The non-existence of an equilibrium stems from the fact that the manufacturers’ instant profits are discontinuous functions of their production capacities. This discontinuity leads to a major technical difficulty in that one cannot apply standard optimal control approaches to study the equilibria of the dynamic game. Our results illustrate the possibility that competition between supply chains might not be sustainable when they sell complementary products and rely on a revenue-sharing agreement.

Dynamic game research of food agricultural products supply chain based on blockchain traceability technology

PurposeFood quality and safety issues have always been imperative topics discussed by people. The anti-tampering of blockchain technology and the transparency of information make it possible to improve food traceability and safety quality. How to effectively apply blockchain traceability technology to food safety has great research significance for improving food safety and consumer quality trust.Design/methodology/approachThe paper aims to analyze the differences in product quality levels and market participants’ profits before and after the use of blockchain-driven traceability technology in the food agricultural product supply chain (SC) in the dynamic game frameworks of supplier-led and retailer-led modes, respectively, and explores the willingness, social welfare and consumer surplus of each member of the agricultural product SC to participate in the blockchain. Besides, We investigate the SC performance improvement with the mechanism of central centralized decision-making and revenue-sharing contract, compared to the SC performance in dynamic games.FindingsThe results are obtained as follow: The adoption of blockchain traceability technology can help improve the quality of food agricultural products, consumer surplus and social welfare, but the application and popularization of technology is hindered by traceability technology installment costs. Compared with the supplier leadership model, retailer-led food quality level, customer surplus and social welfare are higher.Research limitations/implicationsHow to effectively apply blockchain traceability technology to food safety has great research significance for improving food safety and consumer quality trust.Practical implicationsFood quality and safety issues have always been hot topics discussed by people. The anti-tampering of blockchain technology and the transparency of information make it possible to improve food traceability and safety quality.Social implicationsThe research results enrich the theories related to food safety and quality, and provide a valuable reference for food enterprises involved in the decision-making exploration of blockchain technology.Originality/valueBased on the characteristics of blockchain technology, the demand function is adjusted and the product loss risk of channel members is transferred through a Stackelberg game SC composed of agricultural products suppliers and retailers.Highlights:•We introduce two features of blockchain: quality trust and product information tracking.•The willingness of each member of the supply chain to use blockchain for product traceability was explored.•The overall traceability effect of the retailer-led blockchain is better than that of the manufacturer-led blockchain.•The cost of blockchain technology is a barrier to its adoption.•Blockchain brings higher consumer surplus and social welfare.

Vulnerability and Defence: A Case for Stackelberg Game Dynamics

This paper examines the tactical interaction between drones and tanks in modern warfare through game theory, particularly focusing on Stackelberg equilibrium and backward induction. It describes a high-stakes conflict between two teams: one using advanced drones for attack, and the other defending using tanks. The paper conceptualizes this as a sequential game, illustrating the complex strategic dynamics similar to Stackelberg competition, where moves and countermoves are carefully analyzed and predicted.

How does environmental policy affect operations and supply chain management: A literature review

Governments in many countries actively carry out various policies to tackle pollution problems sourced from operations and supply chain activities, aiming at reducing adverse environmental impact and promoting sustainable development. This study provides a comprehensive and well-structured review of research on operations and supply chain management within the context of environmental policy. Specifically, this study meticulously identifies 137 papers and presents the descriptive results of a bibliometric analysis on these papers. Afterwards, using a well-defined framework encompassing three types of policies and various levels of operational and supply chain management, the identified papers are further classified. For each classification, content analyses are conducted accordingly, delving into the diverse concerns and contributions of the reviewed papers from the perspectives of pricing, production planning, inventory and technology management, coordination and competition, recycling and remanufacturing activities, transportation decisions, and network design. Three aspects of sustainability performance are also considered in the analyses. Finally, this study provides future research directions from seven perspectives: research methodology, forms of regulation, dynamic games, types of contracts, sustainable target management, green behavior of supply chain members, and investment constraints. These insights in turn inform the development of policies and decision-making processes related to environmental sustainability.

Edge computing in Internet of Vehicles: A federated learning method based on Stackelberg dynamic game

With the development of Intelligent Transportation Systems (ITS), data on the Internet of Vehicles (IoV) is increasing day by day. To alleviate computing pressure in IoV, Vehicle Edge Computing (VEC) is being widely used as a new computing paradigm. Moreover, to address the serious problem of privacy leakage in VEC, Federated Learning (FL) is increasingly considered for analyzing big data in VEC. However, in actual VEC, problems such as data heterogeneity and poor training often occur. To address this set of problems, we introduce a two-stage Stackelberg game structure for FL training, choosing the Cloud Server (CS) as the leader and the Roadside Unit (RSU) as the follower. Then, we define the utility functions of CS and RSU and obtain the optimal reward rate and local accuracy for each iteration. To address the problem of inefficiency during learning process, we separate high-dimensional data features into global features and personalized features based on feature separation, and use them to capture historical information. Next, vehicle federated learning with historical information based on dynamic Stackelberg game (VFLHI-DSG) was proposed. Finally, we conducted a comprehensive comparative experiment, results show that VFLHI-DSG has excellent performance in different scenarios.

Improved socio-emotional skills in students with autism spectrum disorder (ASD) following an intervention supported by an augmented gamified environment

This study examines the impact of an intervention using an Augmented Gamified Environment (AGE) to stimulate socio-emotional skills in a sample of 54 subjects with Autism Spectrum Disorder (ASD) aged between 3 and 17 years old. The study used a quantitative, exploratory, analytical methodology. Socio-emotional skills were evaluated before and after intervention (pre-posttest) using the DiagnosticApp instrument, supported by a fun app. The study specifically analyzed their ability to identify primary and secondary emotions and emotional states, as well as the cause-effect relationship linked to a context. The results show that socio-emotional skills improved after the intervention, regardless of gender, age, degree of ASD, comorbidity, or type of language. Overall, the greatest improvement was in identifying both primary and secondary emotions through recognizing facial expressions. Additionally, as expected, older students, and those with less severe ASD and more functional language exhibited higher scores in their socio-emotional skills. In conclusion, the extrinsic motivation associated with the mix of game mechanics, dynamics, and aesthetics, along with the augmented reality resources making up the AGE, are key contributing elements in improving these students’ socio-emotional skills.

Network power and firm innovation: the moderating roles of power distance and procedural justice

PurposeThis study aims to investigate the influence of network power on exploratory and exploitative innovation and examines the moderating effects of power distance and procedural justice on these untested relationships.Design/methodology/approachThis study uses survey data collected from firms in China and explores the influential mechanisms of network power, power distance and procedural justice in firm innovation.FindingsThis study empirically shows that network power has an inverted U-shaped effect on exploratory and exploitative innovation. Power distance weakens the effect of network power on exploratory and exploitative innovation, and procedural justice enhances the effect of network power on exploratory and exploitative innovation.Research limitations/implicationsThis study extends resource dependence theory and contributes to the literature on innovation management. Future studies should use different collection channels or research methods to provide more evidence for model promotion. In addition, the dynamic power game among network members and the roles of other mediators or moderators warrant further consideration.Practical implicationsManagers should exercise power strategies properly and ensure that their innovation income exceeds expenditures. Managers need to pay serious attention to power distance and procedural justice in the network and formulate suitable cooperation strategies based on actual conditions.Originality/valueThis study applies the resource dependence theory to investigate the influence of network power on exploratory and exploitative innovation. In addition, the moderating roles of power distance and procedural justice in the above relationships, which have rarely been discussed in previous studies, were tested.

Less is more? An analysis of end time limits in individual divisions at international Boccia events

ABSTRACT The strategic throwing of balls in Boccia matches is influenced by the end duration, prompting athletes to consider their moves carefully. Implementing different end’s time limits could enhance game dynamics, motivating athletes to elevate their performance and engage the audience further. Therefore, this study aims to assess the suitability of the pre-established time limit for each end in Boccia across individual divisions (BC1, BC2, BC3, and BC4) by analysing their remaining unused time. A total of 784 matches from international competitions, including the Americas’ Championship, Asian and Oceania Championship, European Championship, and World Championship, were examined. Findings suggest the potential for a one-minute reduction in the currently established time for BC1 and BC2 divisions. A decreased time limit could enhance the appeal of Boccia for spectators, media, and sponsors.

Models for dual-channel remanufacturing supply chain with reference price effect under static and dynamic games

With the diversity of shopping styles, reference prices have become a consideration in consumers’ purchasing decisions. It is critical to understand how manufacturers and retailers make optimal decisions based on consumer behavior. To this end, we develop a manufacturer-led Stackelberg (M-Stackelberg) game model to investigate the impact of consumer proportion, reference price effect (RPE), and the channel preference coefficient on the decision of the remanufacturing supply chain (RSC) in dual-channel structures. Through comparing different game scenario models, we find that when the reference price coefficient is relatively small, the optimal decisions for the manufacturer and the retailer are the same regardless of whether the RPE is considered. The manufacturer and E-tailer always benefit from RPE, while the traditional retailer (T-retailer) is uncertain. The numerical analysis revealed that the profits of supply chain members are inversely proportional to the proportion of consumers. The smaller the proportion of primary consumers, the more favorable the supply chain. In particular, the higher the channel preference coefficient, the higher the profits of the manufacturer and E-tailer, while the lower the benefit of the T-retailer. Further, in the dynamic game, the total supply chain profit is highest when the T-retailer prices earlier than the E-tailer.

Optimization of Service Utility in 5G Heterogeneous Networks Using Dynamic Game

Optimization of Service Utility in 5G Heterogeneous Networks Using Dynamic Game

Incidence of injuries and their prevention in Czech ice hockey players.

Ice hockey is a dynamic game. We can observe collisions between the players that bring a risk of injury. There are many hockey clubs in the Czech Republic. These clubs raise great hockey players and many competing players in various levels of national leagues. The aim of this study was to map injuries in Czech hockey players and outline the situation of injury prevention and body care in ice hockey players. We used a questionnaire survey method to obtain data. We received answers from 100 male active Czech ice hockey players, playing in the top three highest men's competitions (Extraleague - 2nd league). Individual injuries were analyzed according to specific body parts, injury type, playing position, level of competition using basic statistical characteristics and relative frequency analyses, including the recovery time, injury reason and the injury statistics per 1000 sporting performances in ice hockey. We found that 81% of participants suffered injuries with the overall incidence of injuries was 17.1 per 1000 sports performances and mainly happened during the match compared to training. The most common injuries were in the head and neck area (25%), often caused by a collision with another player, a stick or puck hit, or a collision with a board. Other frequently injured parts were the knees (21%), where internal ligament injuries predominate, and the shoulders (20%), where we recorded mainly ligament injuries. There is a high risk of various injury types of ice hockey players, that are developed accidentally in all body parts mostly in the match (mostly upper part of the body and knee) or by overloading (hip/groin area). We recommend strategies to avoid or minimize the injury risk of players. The hockey clubs, coaches, and players should extensively and regularly cooperate with physiotherapists, starting from the younger age of hockey groups, to prevent injuries and use regular strengthening of crucial muscle parts, regeneration, and compensatory exercises. We endorse adequately evaluating dangerous foul actions for referees and disciplinary officials also in minor competitions.

Network defense decision-making based on deep reinforcement learning and dynamic game theory

Network defense decision-making based on deep reinforcement learning and dynamic game theory

The Stochastic Evolution Game of Knowledge-Sharing Incentive in Virtual Communities under Intelligent Recommendation Systems

To effectively solve the issue of unsmooth knowledge sharing in virtual communities under intelligent recommendation systems, we analyzed the impact of key factors on the strategy selection and evolution path in different scenarios.Based on the principles of bounded rationality and benefit maximization, we consider the principles of evolutionary game theory and the influence of random interference. A random evolutionary game model is constructed to analyze strategy selection in the process of knowledge sharing incentives between virtual community platforms and users. We obtained the evolutionary equilibrium strategies under different parameter restrictions and analyzed the evolutionary stability of the dynamic game process of knowledge sharing incentives.The research shows that interference from random factors affects both the speed and the trend of strategy evolution in virtual community platforms and users. In order to improve the enthusiasm of users to share, virtual community need to increase the proportion of users with positive feedback, improve the recommendation incentive mechanism, and reduce the user loss coefficient. Based on the above research conclusions, some countermeasures and suggestions for improving the performance of virtual community knowledge sharing under intelligent recommendation systems are proposed, which provides theoretical guidance for knowledge sharing among virtual community members.

Navigating the personal carbon inclusion scheme: An evolutionary game theory approach to low-carbon behaviors among socio-economic groups

In response to the challenges posed by climate change, China has launched the Personal Carbon Inclusion (PCI) scheme to encourage individuals to transition towards low-carbon lifestyles. This study investigates the behaviors of participants within the PCI scheme using a tripartite evolutionary game model, encompassing high-income and low-income individuals, as well as the PCI platform itself. The research analyzes participants' strategies, examines the evolutionary stability of different strategies, and assesses the robustness of equilibrium points within the game dynamics. Key findings reveal: (1) High-income participants tend to be less willing to adopt low-carbon behaviors compared to low-income participants. (2) The PCI platform displays limited proactive engagement in promoting low-carbon policies. (3) Factors, particularly the cost and pricing mechanisms of low-carbon actions, significantly impact the evolutionary progression of the system. Moreover, practical recommendations are provided to enhance the effectiveness of PCI schemes.

The impact of carbon emission regulations on B2C car-sharing platforms’ operating models

PurposeAlthough the impact of carbon emissions regulations is evident to upstream automakers, their influence on downstream B2C car-sharing platforms remains unclear. This article reveals the influence of carbon emission regulations on the performance of supply chain members. In particular, we focused on the decision of B2C car-sharing platforms.Design/methodology/approachWe develop a three-stage dynamic game model consisting of an automaker, a B2C car-sharing platform and consumers.FindingsThe carbon emission cap has a critical threshold. Above this threshold, the regulation is ineffective for the platform’s operating model. Below it, the regulation affects the platform, moderated by customers' green awareness. The threshold initially decreases (weakly) and then increases in awareness. Effective caps reduce profits for the manufacturer, B2C car-sharing platform and supply chain, while ineffective caps see higher profits with increased awareness.Originality/valueFirstly, this paper explores the impact of carbon emission caps on the operational strategies of B2C car-sharing platforms within the sharing economy, complementing existing research. Secondly, it identifies conditions where stricter caps prompt B2C car-sharing platforms to adjust their operational models and offers fresh insights for managers and departments responsible for carbon emission policy formulation. Thirdly, the study uncovers how carbon emission caps affect the performance of supply chain members, providing crucial managerial insights for sustainable operations.