Game Model Research Articles

Fairness mechanism and stackelberg strategy for multi-agent systems: A case study of legends of the three kingdoms

Alongside the rapid advancement of artificial intelligence technologies, the complexity of society continues to escalate, and the design of multi-agent system rules becomes increasingly crucial, optimize participant engagement and addressing the issue of fairness and equilibrium win rates. The card game Legends of the Three Kingdoms (LTK), as a complex multi-agent system, represents an important abstraction of real-world scenarios, requiring the implementation of proper incentive mechanisms. Based on the mechanism and Stackelberg, this paper optimizes player strategies and system fairness. Firstly, we constructed a multi-agent Stackelberg game model for team battles. Then, we analyzed the impact of decision-making factors on players. Subsequently, we defined three kinds of fairness and improved the incentive mechanism. The results indicate that our mechanism optimizes participants' game behaviors, enhancing fairness among team players. Win rates were improved from 56.2% VS 43.8% to 51.4% VS 48.6%. With three different fairness measures, the win percentage fairness increased by 72 %, and the first elimination fairness increased by about 79 %. Our research provides a reference for understanding and analyzing complex computational models and facilitates the resolution of various resource allocation and system design issues.

Incentive mechanism and scenario simulation of residential energy-efficiency retrofits – From the perspective of tripartite evolutionary game

Energy-efficiency retrofits (EER) are increasingly becoming a key tool for sustainable building development. Compared to extensive urban renewal, refined building energy retrofits hold more practical value. Of this, the complexities arising from the differences in the claims of multiple stakeholders deserve our attention. However, limited efforts have been made in the existing literature to explore this issue. This paper constructs a tripartite evolutionary game model for residential EER from the perspective of engineering management. Taking a typical building in an old neighborhood in Nanchang, Jiangxi Province as an example, the theoretical model is validated. The results indicate that participants in the residential EER market display varying decision-making behaviors at different developmental stages. The government’s implementation of appropriate punitive measures in the early stages will encourage enterprises to participate in EER. Simultaneously, attention should also be paid to the demands of residents to ensure the smooth progress. Market-based renovation models should be actively promoted, and specific renovation programs should be created to accommodate varying requirements. This paper offers theoretical guidance for decision-making and developing residential EER.

Carbon tax for energy-intensive enterprises: A study on carbon emission reduction strategies

With the implementation of the carbon tax policy, the carbon emission reduction (CER) actions taken by leading enterprises in energy-intensive industries will significantly influence the CER decisions of their following firms. To delve into the boundary conditions of leading and following enterprises’ CER strategies, this paper constructs three tailored CER decision-making game models, specifically targeting leading and following enterprises in these industries. These models are designed to compare and analyze the impact of carbon tax on various CER decision modes. The study mainly derives: (1) Carbon tax is not always conducive to boosting the carbon reduction efforts of both corporations. Only when the carbon tax is smaller than a certain threshold will the carbon abatement efforts of leading and following corporations be proportional to the tax. Moreover, only when the lead firm abates its carbon emission does it contribute to the degree of carbon abatement effort. (2) The overall profitability of the supply chain (SC) is optimized when only the lead company reduces its carbon emissions. In this scenario, not only does the lead corporation’s carbon reduction efforts increase, but the lead corporation and the followers also realize a win–win profit. (3) The model with the highest carbon abatement effort is not necessarily conducive to the environment. When the unit product carbon abatement emissions of the two corporations are within a certain threshold interval, the ambient impact of carbon abatement by only the leading firm is greater than that of no abatement by both corporations. The effect on the environment is minimized when both corporations make CER.

Tripartite evolutionary game and simulation analysis of electric bus charging facility sharing under the governmental reward and punishment mechanism

Electric vehicles (EVs) are environmentally friendly with the features of low noise levels and zero tailpipe emissions. However, limited charging facilities have restricted the large-scale development of EVs, and electric bus charging facility sharing is a promising solution to this issue. While reducing charging time and improving facility utilization, this measure involves the interests of the government, bus operators, and electric car owners, requiring a systemic analysis of their interactions. Therefore, this study constructs a tripartite evolutionary game model under the governmental reward and punishment mechanism. The model examines the strategic decision-making process, influential factors, and evolutionary stability of three players, followed by simulation analysis. The results show that: (1) The evolutionary system may exhibit three stable states: (0,0,0), (1,0,0) and (1,1,1), and enhance the initial ratio of the three stakeholders will help evolve towards the ideal state. (2) Increasing rewards and penalties can both be meaningful, when penalties exceed rewards, the measures can be more effective. (3) Bus operators are more sensitive to incentive and penalty measures than electric car owners, and governments should pay more attention to them in the implementation process. The findings can provide references for the policy formulation on electric bus charging facility sharing.

Settlement Selection Strategic Analysis for Self-Operated E-Commerce Platforms under Market Competition

This paper focuses on the settlement selection strategic analysis for self-operated e-commerce platforms on hybrid e-commerce platforms under market competition. Taking factors such as the market share, price competition, commission, and customer loyalty into account, a multi-leader–follower game model with the platforms as leaders and the manufacturers as followers is established. Then, we solve the model with the help of some mathematical techniques and describe some numerical experiments to analyze settlement strategies for the self-operated platforms and their impact on other members in the network. The numerical results reveal the following revelations: a lower commission rate is more suitable for the self-operated platforms; once the commission rates are determined, the self-operated platforms prefer to settle in the hybrid platforms under lower medium price competition; when the price competition is fierce, as customer loyalty increases, the self-operated platforms should settle with a low market share; if the self-operated platforms settle in the hybrid platforms, then a higher price competition is advantageous for all members and can facilitate supply chain coordination.

Investment and remanufacturing strategies considering the application of intelligent manufacturing in hybrid manufacturing–remanufacturing systems

The development of data science and sensing technologies provides opportunities to mitigate uncertainty in hybrid manufacturing–remanufacturing systems, and drives manufacturers to invest in intelligent manufacturing (IM). This paper considers the adoption of IM to mitigate classification errors in the end-of-use (EoU) products’ acquisition while improving the operational efficiency of manufacturing–remanufacturing systems. By constructing game models, we jointly investigate the investment, pricing, production and order quantities, and collection decisions in a closed-loop supply chain. Interestingly, we find that IM does not always increase manufacturers’ enthusiasm to engage in remanufacturing, firms’ profits or consumer surplus. It does not always reduce environmental impact either. Analytical results show that IM reduces manufacturers’ enthusiasm to engage in remanufacturing if the initial core misclassification rate is low. Furthermore, we identify key factors that impact the firms’ profits, consumer surplus, and carbon emissions. For a manufacturer producing high-cost new products, investing in IM hurts its profits when the remanufacturing cost savings due to intelligent manufacturing is small and the manufacturing benefit due to IM is not significant. Moreover, investing in IM reduces consumer surplus if the cost of new products is high, and the IM does not lead to significant remanufacturing cost saving and manufacturing benefit increase. The results reveal that investing in IM is preferred from the environmental point of view if the IM-induced manufacturing cost saving is small. Our research provides management insights into the intelligent transformation of manufacturers with hybrid manufacturing–remanufacturing systems, as well as policymakers concerned with value creation for customers and environmental impacts.

The Impact of Transaction Credit on Credit Enhancement of Supply Chain Financing of Small and Micro-Logistics Based on Evolutionary Game Analysis

The issue of credit enhancement in supply chain financing for small and micro-logistics enterprises (SMLEs), as well as the factors that affect the decision-making of participants in supply chain financing transaction credit enhancement, is analyzed in this study. First, an evolutionary game model between financial institutions (FIs) and SMLEs was built. In contrast to bank loans, a novel mechanism for achieving credit enhancement based on transaction data in the transportation supply chain was established through a strict environment and an increase in default penalties to compel SMLEs to uphold their obligations. Furthermore, the stability analysis shows that the stable state convergence of the evolutionary game between FIs and SMLEs evolves to the stage where FIs offer loans to SMLEs. Finally, according to the simulation analysis on the real data collected from CHZL logistics park survey data, this work demonstrates that the fluctuation ranges of the strategy evolution process for the FIs and SMLEs are positively correlated with the intensity of the stochastic perturbation.

Tripartite Evolutionary Game Analysis of Product Quality Supervision in Live-Streaming E-Commerce

With the rapid development of information technology, live-streaming e-commerce has risen rapidly as a new business model. However, product quality problems that exist in the development of live-streaming e-commerce continue to emerge. The influence of strategic interactions between social media influencers, live-streaming e-commerce platforms, and consumers on product quality deserves to be studied. Therefore, this paper constructs a tripartite game model of “social media influencers–the live-streaming e-commerce platform–consumers” and analyzes the dynamic evolution process of the strategy selection among subjects and influencing factors by using evolutionary game theory. This study shows that products with high functional value are more likely to stimulate consumer rights protection behavior, prompting social media influencers to shift from lax to strict quality control. But when the emotional value is high, consumers are more inclined to give up on defending their rights, which leads to the maintenance of lax quality control, and the platform supervision will be weakened accordingly. Moreover, less quality differences motivate social media influencers to choose lax quality control. An increase in quality differences will promote a shift from an equilibrium strategy to strict quality control. However, if the penalty of the platforms is not strong enough, this strategic shift will not happen. In addition, a high percentage of platform commissions can encourage influencers to implement strict quality control, while platforms can maintain weak supervision. This study’s findings provide valuable guidance for understanding and managing product quality issues in live-streaming e-commerce. In the future, the government will be considered a new player in the game in studying the impact of its policies on product quality in live-streaming e-commerce.

Optimal Bidding Strategies for Wind-Thermal Power Generation Rights Trading: A Game-Theoretic Approach Integrating Carbon Trading and Green Certificate Trading

In response to the challenges of low wind power consumption and high pollution emissions from thermal power, the implementation of wind-thermal power generation rights trading is a proactive attempt to reduce wind power curtailment and promote its consumption. This study first regards the alternating bidding process between the two parties as a dynamic game, using the Rubinstein bargaining game model to determine the incremental profit allocation and optimal bidding for both parties in power generation rights trading. Secondly, an energy conservation and emission reduction model is constructed to analyze the benefits from the perspectives of standard coal consumption saving and the carbon emission reduction caused by power generation rights trading. Finally, a combined trading revenue model is established to analyze the final profit of both parties involved in the trading. The results show that the combined trading of wind-thermal power generation rights, incorporating carbon trading and green certificate trading, can effectively promote coal consumption savings in thermal power units and reduce the carbon emissions of the power industry. Moreover, it significantly increases the final profit for both parties, stimulating the enthusiasm of generators for participating in power generation rights trading, and ultimately promoting wind power consumption.

3D Unity Labyrinth Game Model Based on Android as an Educational Media in Improving Knowledge and Teeth Brushing Skills in Deaf Children

Deaf children tend to have a higher frequency of caries than non-deaf children. Deaf children have limitations in their sense of hearing when capturing information. Dental health education in a promotional way is one strategy that can be used to provide behavior change for deaf children. Promotives using visual methods are very suitable because they have high visual capture power. One of the visual methods is endgame. The technique used is Research and Development with a quick experiment Pretest-Posttest group design research design. The subjects in this research were deaf students at SLBN Gorontalo City. Intervention: 10 people were given the Android-based 3D Unity Labyrinth Game, and control of 10 people was given conventional methods. Data collection techniques include: questionnaires and observation of tooth brushing and DI examination. Data was tested using the Paired Sample T Test and Independent Sample T Test. The results obtained are that the Android-based 3D Unity Labyrinth Game Model can increase knowledge of brushing teeth and brushing skills in deaf children and reduce the debris index in deaf children. The Android-based Unity 3D Labyrinth Game Model is effective as a learning medium for improving knowledge of brushing teeth and brushing skills in deaf children.

Impact of cap-and-trade mechanism on investment decision of new electric power system.

Under the background of cap-and-trade mechanisms, this article constructs a game model of the electricity supply chain, which is dominated by electricity generators and followed by electricity sellers, taking into account the situation of electricity generators investing in renewable energy and energy storage under the grandfathering mechanism (GM) and benchmarking mechanism (BM). By comparing the equilibrium solutions in different cases, the research finds that (1) compared with the grandfathering mechanism, the benchmarking mechanism has more investment in renewable energy and higher energy storage quality; (2) in the consumer market, compared with GM, the electricity price and the electricity demand are higher under BM; (3) an increase in the renewable energy preference coefficient or carbon price will lead to an increase in the electricity wholesale price, renewable energy investment, energy storage quality, electricity price, and electricity demand. Further, an increase in the energy storage cost coefficient or renewable energy investment cost coefficient will result in lower electricity wholesale price, renewable energy investment, energy storage quality, electricity price, and electricity demand; and (4) the profit of the generator under GM is higher than that under BM when the total carbon quota is larger, while the profit of the generator under BM is higher than that under GM when the unit carbon quota is larger.

Analysis of charging tariffs for residential electric vehicle users based on Stackelberg game

Establishing a rational pricing mechanism for electric vehicles (EVs) can incentivize users to engage in charging activities, foster positive consumption behaviors, and indirectly benefit the grid by increasing load demand. Therefore, this paper conducts a Stackelberg game study between the grid and EV users by utilizing real charging and discharging data of EV users in F city. First, the price elasticity of EV users' electricity consumption behavior is analyzed. Second, the Stackelberg game model is constructed, multiple tariff schemes are designed to calculate the equilibrium tariff of the game, and the benefits of the grid and EV users are analyzed in comparison with the tariff policy that will be implemented in F city. Lastly, different seasonal scenarios are constructed to extend the applicability of the research results. It is found that Scheme 3 effectively incentivizes charging load growth, increases cross-subsidies and transmission and distribution fees, and protects the level of charging and discharging costs for residents; furthermore, lowering charging and discharging tariffs during seasons of high price elasticity for residents to increase demand is an optimal strategy for grid pricing.

Differential games in the supply chain of innovative products with consumer purchase regret induced returns.

Innovative products entering the market will cause dynamic changes in market demand, and consumers' purchase regret and their return behavior make the market environment more and more complex, which in turn affects the dynamic decision-making in the supply chain. In this paper, under the situation of discrete decision time, combining with the objective reality, we make discrete modification to the classical Bass diffusion model (Bass model), construct a manufacturer-led, retailer-followed supply chain differential game model, analyze the optimal decision-making of the manufacturer and the retailer by combining with the theory of discrete optimal control, and then verify the conclusions by numerical simulation. The results show that: when retailers purchase directly from the manufacturer and sell in the market, the optimal pricing of the innovative product can make the supply chain as a whole, realizing Pareto optimality; consumer's purchase regret will increase the amount of returns, which will lead to the decrease of product sales and the profits of the manufacturer and the retailer; when the innovative product accounts for a different share of the market, the impact of purchase regret on the wholesale price and the retail price are also different. Therefore, manufacturers need to have an extensive comprehension of the market to minimize the negative effects of consumer regret and returns, and to formulate a reasonable pricing strategy for their products to gain as much profit as possible.

The effect of nonlinear environmental feedback on the outcomes of evolutionary dynamics

In this paper, we construct a nonlinear evolutionary game model to analyze the cooperation mechanisms of the population based on a nonlinear relationship among environment and strategies. In the model, replicator dynamics and aspiration dynamics are used to explore the evolutionary outcomes of collective decision, respectively. The results suggest that the environment tends to become progressively more affluent as the number of cooperators increases, if there is a smaller intensity of environmental destruction of defectors. Interestingly, the enriched environments may attract more defectors. Hence, the population requires a higher level of vigilance against plentiful environments in response to the emergence of defectors. As opposed to replicator dynamics, aspiration dynamics can avoid the persistent oscillatory loops due to the level of aspiration. Further, we investigate the effect of complexity between the population strategy and the environment on the evolutionary outcomes. It is found that higher level of complexity can drive the environment closer to a state of affluence, but the population's strategy structure will not be modified. These insights into the relationship between environment and strategies further our understanding of the evolutionary mechanism of population and society.

Academic publication uncertainty and research behavior

AbstractThere are many uncertainties in the production/dissemination of academic research. This paper incorporates publication uncertainty in a game model between researchers and journal editors, and examines its effects on the quantity and quality of research and on citations. Authors seek to maximize satisfaction from their publishing efforts, while journal editors try to enhance reputations of their journals. Publication probability depends on the number of academic journals. Results show that the impacts of a change in the number of journals (capturing publication uncertanty) on citations and quality are symmetric. Citations and research quality can go up, while total publications (research quantity) can increase, decrease, or stay unchanged.

Coordinated Multi-Scenario Optimization Strategy for Park Photovoltaic Storage Based on Master-Slave Game.

Optimizing the operation of photovoltaic (PV) storage systems is crucial for meeting the load demands of parks while minimizing curtailment and enhancing economic efficiency. This paper proposes a multi-scenario collaborative optimization strategy for PV storage systems based on a master-slave game model. Three types of energy storage system (ESS) application scenarios are designed to comprehensively stabilize PV fluctuations, compensate for load transfers, and participate in the frequency regulation (FR) market, thereby optimizing the overall operational strategy of PV storage systems in parks. The upper-level objective is to maximize the park operators' profit, while the lower-level objective is to minimize the user's power supply costs. Case studies demonstrate that this strategy can significantly increase the economic benefits for park operators by 25.8%, reduce user electricity expenditures by 5.27%, and lower curtailment through a load response mechanism, thereby promoting the development and construction of PV storage parks.

Low-Carbon Supply Chain Decision-Making and CSR Strategy Evolution Analysis Considering Heterogeneous Consumer Preferences

Decision-making regarding the low-carbon supply chain, considering corporate social responsibility (CSR) and the heterogeneous preferences of consumers, has become an urgent topic to be explored. This paper explores the decision-making problem of a low-carbon supply chain considering the heterogeneous preferences of consumers under different CSR situations, analyzes the influence of important parameters on each equilibrium solution, compares the size relationship of each equilibrium solution under different CSR situations, and verifies the conclusions obtained through numerical simulation. Then, based on the obtained equilibrium solution, a CSR evolutionary game model of the low-carbon supply chain is constructed, and the evolutionary stability strategies of the two sides on the CSR game are solved. Finally, the evolutionary trajectory of the game system is intuitively presented using a simulation method, and the influence of the main parameters on the evolutionary trends of the two sides is analyzed. The findings are as follows: (1) When both manufacturers and retailers undertake CSR, the retail price and wholesale price are their lowest, while carbon emission reduction, total market demand, manufacturer utility, retailer utility, and supply chain total utility are the highest. (2) When a company undertakes CSR, carbon emission reduction, total market demand, manufacturer utility, retailer utility, and supply chain total utility all increase with the increase in the CSR degree of the company and the ratio of the potential scale of low-carbon consumers to the potential scale of ordinary consumers. (3) The evolutionary stability strategy for both manufacturers and retailers is to undertake CSR. In addition, the initial proportion of manufacturers and retailers that undertake CSR, the low-carbon preference of low-carbon consumers, and the increase in the ratio of the potential scale of low-carbon consumers to the potential scale of ordinary consumers can encourage both members of the supply chain to undertake CSR.

Defense strategy selection based on incomplete information game for the false data injection attack

With the rapid development and wide application of sensing devices and communication networks, the traditional power system has transformed into a cyber physical power system (CPPS) gradually. The constant interaction of information flow and power flow exposes the grid to potential cyber-attack risks. In this paper, the defense strategy selection approaches are proposed based on incomplete information game against false data injection attack (FDIA) in different scenarios. Firstly, the attack-defense tree model containing economic indicators and a measure of attack is established, and the expected revenues of both attacker and defender are calculated in detail. Secondly, the static Bayesian attack-defense game model in which the defender grasps incomplete information is constructed, considering two cases of low-tech attacker and high-tech attacker. Then, the zero-sum attack-defense game model in which the attacker masters incomplete information is structured, considering the changing attack space. Finally, the simulations are carried out on the IEEE 30-bus system, and the optimal defense strategies in the case of two incomplete information are obtained by solving the equilibrium point. The simulation results demonstrate that the proposed method is effective in cyber security defense system, and can provide guiding ideology and theoretical basis for operators to deploy defense measures.

Prevention and adaptation of intermodal interactive seaports and dry ports under asymmetric risk behavior

The port-hinterland system, encompassing seaports and dry ports, has evolved into the backbone of international trade. Due to their unique geographic locations and critical socioeconomic functions, ports are particularly susceptible to a range of risks. Port authorities (PAs) can address these challenges through targeted preventive efforts, which aims to reduce the probability of risk occurrence, and adaptive efforts, which seeks to mitigate potential damage. However, intermodal interactions and the asymmetric risk behaviors exhibited by ports under risk probability ambiguity present significant challenges for PAs making risk-responsive investments. This study develops a two-stage game model to examine the effects of asymmetric risk behavior and risk probability ambiguity on strategic investment decisions. Our analysis reveals that prevention are susceptible to free-rider effects, which are further exacerbated by risk behaviors and mitigated by investment strategy differentiation. Moreover, we demonstrate that, as a general guideline, seaport authorities should prioritize adaptation, while dry port authorities should focus on prevention, with adaptation being the primary strategy when the level of risk aversion is low. These findings provide valuable managerial insights for improving the risk management and resilience of the port-hinterland system.

Research on Division of Labor Decision and System Stability of Swarm Robots Based on Mutual Information.

In rational decision-making processes, the information interaction among individual robots is a critical factor influencing system stability. We establish a game-theoretic model based on mutual information to address division of labor decision-making and stability issues arising from differential information interaction among swarm robots. Firstly, a mutual information model is employed to measure the information interaction among robots and analyze its influence on the behavior of individual robots. Secondly, employing the Cournot model and the Stackelberg model, we model the diverse decision-making behaviors of swarm robots influenced by discrepancies in mutual information. The intricate decision dynamics exhibited by the system under the disparity mutual information values during the game process, along with the stability of Nash equilibrium points, are analyzed. Finally, dynamic complexity simulations of the game models are simulated under the disparity mutual information values: (1) When ν1 of the game model varies within a certain range, the Nash equilibrium point loses stability and enters a chaotic state. (2) As I(X;Y) increases, the decision-making pattern of robots transitions gradually from the Cournot game to the Stackelberg game. Concurrently, the sensitivity of swarm robotics systems to changes in decision parameter decreases, reducing the likelihood of the system entering a chaotic state.