Game Theory Research Articles

Zero-Trust Zero-Communication Defence against Hybrid Cyberattacks in Distributed Energy Resources Using Mean Field Reinforcement Leaning

As the evolution of smart grids accelerates, distributed energy resources (DERs) emerge as key elements in the transformation of global energy systems. However, the integration of these technologies introduces significant cybersecurity vulnerabilities, notably false data injection (FDI) and a direct load-altering attack (DLAA). Traditional load-altering attacks require a huge attack load and, thus, are not practical to implement. In contrast, in modern DER environments where households become “prosumers” with high-power energy generation, the implications of such attacks are substantially amplified. This paper considers a hybrid cyberattack that includes both FDI and a DLAA, and presents a hierarchical, optimal load adjustment framework that addresses these security concerns. A centralized optimizer first calculates the ideal load-shedding strategies for each substation, which are then securely broadcast to households. To address the complexities at the individual household level, we introduce a novel reinforcement learning algorithm termed Mean Field Deep Deterministic Policy Gradients (MF-DDPG). This algorithm employs mean-field game theory to enable decentrally coordinated decision-making among each household, making it particularly effective in zero-trust scenarios. Through this multifaceted approach, we offer a robust countermeasure against load-altering attacks, thereby enhancing the resilience and stability of advanced smart grids.

COOPERATIVE THEORY OF THE SECOND HALF OF THE XIX – FIRST HALF OF THE XX CENTURIES

The article is devoted to the analysis of the theoretical views of thinkers representing various directions of socio-political thought on cooperation, its place and role in social development. The views of representatives of the Marxist, populist, and social democratic directions of the science of cooperation are specially considered, an idea is given about the theoretical concepts of the Italian and American academic communities of cooperation researchers, and the contribution of intellectuals developing game theory.

Optimization of offshore wind farm cluster transmission system topology based on Stackelberg game

Offshore wind energy is pivotal in the global energy transition, with a global installed capacity reaching 64.3 GW by 2022 and an expected annual increase of 60.2 GW over the next decade. This study aims to optimize the topology of transmission systems (TS) for offshore wind farm (OWF) clusters using Stackelberg game theory. The OWF investor (OWFI) acts as the leader, optimizing investment returns while considering wake effects, and the offshore TS operator (OTSO) follows by adjusting transmission strategies to reduce costs. The analysis includes the wake effects within OWF clusters and their impact on power generation efficiency. Simulation results demonstrate that the proposed model can balance stakeholder interests and enhance the economic viability of OWF clusters, showing a potential increase in net present value (NPV) by up to 30 %. This study validates the practical application of the Stackelberg game model in optimizing OWF cluster TS topology, contributing to more efficient and cost-effective renewable energy integration.

The potential use of game theory in decision-making in CHD.

Background: Congenital cardiac care involves multiple stakeholders including patients and their families, surgeons, cardiologists, anaesthetists, the wider multidisciplinary team, healthcare providers, and manufacturers, all of whom are involved in the decision-making process to some degree. Game theory utilises human behaviour to address the dynamics involved in a decision and what the best payoff is depending on the decision of other players. Aim: By presenting these interactions as a strategic game, this paper aims to provide a descriptive analysis on the utility and effectiveness of game theory in optimising decision-making in congenital cardiac care. Methodology: The comprehensive literature was searched to identify papers on game theory, and its application within surgery.Results: The analysis demonstrated that by utilising game theories, decision-making can be more aligned with patient-centric approaches, potentially improving clinical outcomes. Conclusion: Game theory is a useful tool for improving decision-making and may pave the way for more efficient and improved patient-centric approaches.

Feature selection based on game theory optimization to achieve desired performance metrics in seizure onset detection

Background and Objective: Epilepsy is one of the common diseases of the nervous system, which affects almost 1% of the world’s population. The unpredictable nature of epileptic seizures has caused people suffering from it to be deprived of their normal life, and making a device that can detect a seizure onset can help them. Methods:Game theory is a branch of mathematical science that, after proving its ability in economics, has entered into the field of signal processing and is trying to solve complex problems with a new approach. In this paper, we use game theory and coalitional game concepts to provide a novel way of feature selection in the analysis of Electroencephalography (EEG) signals. We have used a variety of statistical, morphological, and frequency features, and with the proposed feature selection algorithm we have attempted to select the smallest coalition which discriminates between two brain states while appropriately allocating resources to satisfy our desired sensitivity, delay, and false alarm. A modified change point detection algorithm has also been introduced to be used to detect epileptic seizures. Results:The results of the test on the CHB-MIT dataset show that using the proposed algorithm, we can achieve improved performance in terms of sensitivity, delay, and false alarm with a few number of features. Our framework also provides a means to focus on desired criteria for different applications. In scenario which the focus was on sensitivity, the proposed framework achieved 99% average sensitivity, 0.4/h average false alarm, and 2.4 s average delay with only using about 2 features for each patient. Conclusion:By applying the proposed framework on the CHB-MIT dataset we observe that we can achieve better performance compared to recent studies with fewer features in terms of sensitivity, delay, and false alarm metrics. Such an algorithm can be used for the purpose of real-time detection and in wearable devices.

Different strokes in randomised strategies: Revisiting Kuhn's theorem under finite-memory assumptions

Two-player (antagonistic) games on (possibly stochastic) graphs are a prevalent model in theoretical computer science, notably as a framework for reactive synthesis.Optimal strategies may require randomisation when dealing with inherently probabilistic goals, balancing multiple objectives, or in contexts of partial information. There is no unique way to define randomised strategies. For instance, one can use so-called mixed strategies or behavioural ones. In the most general setting, these two classes do not share the same expressiveness. A seminal result in game theory — Kuhn's theorem — asserts their equivalence in games of perfect recall.This result crucially relies on the possibility for strategies to use infinite memory, i.e., unlimited knowledge of all past observations. However, computer systems are finite in practice. Hence it is pertinent to restrict our attention to finite-memory strategies, defined as automata with outputs. Randomisation can be implemented in these in different ways: the initialisation, outputs or transitions can be randomised or deterministic respectively. Depending on which aspects are randomised, the expressiveness of the corresponding class of finite-memory strategies differs.In this work, we study two-player concurrent stochastic games and provide a complete taxonomy of the classes of finite-memory strategies obtained by varying which of the three aforementioned components are randomised. Our taxonomy holds in games of perfect and imperfect information with perfect recall, and in games with more than two players. We also provide an adapted taxonomy for games with imperfect recall.

A complete classification of evolutionary games with environmental feedback

Abstract A tragedy of the commons, in which rational behavior of individuals to maximize their own payoffs depletes common resources, is one of the most important research topics in game theory. To better understand the social dilemma problem, recent studies have developed a theoretical framework of feedback-evolving game where individual behavior affects an environmental (renewable) resource and the environmental resource changes individual payoffs. While previous studies assumed that the frequency of defectors increases (prisoner's dilemma [PD] game) when the environmental resource is abundant to investigate an oscillating tragedy of the commons, it is also possible for other types of game to produce the social dilemma. In this paper, we extend the feedback-evolving game by considering not only PD game, but also the other three game structures when the environmental resource is replete for a reasonably complete classification. The three games are Chicken game where defectors and cooperators coexist through minority advantage, Stag-Hunt (SH) game with minority disadvantage, and Trivial game where the frequency of cooperators increases. In addition, we utilize a dilemma phase plane to visually track (transient) dynamics of game structure changes. We found that an emergent initial condition dependence (i.e. bistability) is pervasive in the feedback-evolving game when the three games are involved. We also showed that persistent oscillation dynamics arise even with Chicken or SH games in replete environments. Our generalized analysis will be an important step to further extend the theoretical framework of feedback-evolving game to various game situations with environmental feedback.

Editorial for the Special Issue: "Novel Solutions and Novel Approaches in Operational Research"

Abstract This special issue of Business Systems Research (SI of the BSR) is being co-published by the Slovenian Society INFORMATIKA – Section for Operational Research (SSI -SOR). It focuses on recent advances in Operations Research and Management Science (OR / MS), with a particular emphasis on linking OR / MS with other areas of quantitative and qualitative methods in the context of a multidisciplinary framework. The ten papers that were chosen for this Special Issue of the BSR present advancements and new techniques (methodology) in the field of Operations Research (OR), as well as their application in a variety of fields, including risk management, mathematical programming, game theory, gravity, spatial analysis, logistics, circular economy, continuous improvement, sustainability, e-commerce, forecasting, Gaussian processes, linear regression, multi-layer perceptron, and machine learning.

Coal-Mine Water-Hazard Risk Evaluation Based on the Combination of Extension Theory, Game Theory, and Dempster–Shafer Evidence Theory

Due to the complex hydrogeological conditions and water hazards in coal mines, there are multiple indexes, complexities, incompatibilities, and uncertainty issues in the risk evaluation process of coal-mine water hazards. To accurately evaluate the risk of coal-mine water hazards, a comprehensive evaluation method based on extension theory, game theory, and Dempster–Shafer (DS) evidence theory is proposed. Firstly, a hierarchical water-hazard risk-evaluation index system is established, and then matter-element theory in extension theory is used to establish a matter-element model for coal-mine water-hazard risk. The membership relationship between various evaluation indexes and risk grades of coal-mine water-hazard risk is quantified using correlation functions of extension set theory, and the quantitative results are normalized to obtain basic belief assignments (BBAs) of risk grades for each index. Then, the subjective weights of evaluation indexes are calculated using the order relation analysis (G1) method, and the objective weights of evaluation indexes are calculated using the entropy weight (EW) method. The improved combination weighting method of game theory (ICWMGT) is introduced to determine the combination weight of each evaluation index, which is used to correct the BBAs of risk grades for each index. Finally, the fusion of DS evidence theory based on matrix analysis is used to fuse BBAs, and the rating with the highest belief fusion result is taken as the final evaluation result. The evaluation model was applied to the water-hazard risk evaluation of Sangbei Coal Mine, the evaluation result was of II grade water-hazard risk, and it was in line with the actual engineering situation. The evaluation result was compared with the evaluation results of three methods, namely the expert scoring method, the fuzzy comprehensive evaluation method, and the extension method. The scientificity and reliability of the method adopted in this paper were verified through this method. At the same time, based on the evaluation results, in-depth data mining was conducted on the risk indexes of coal-mine water hazards, and it was mainly found that 11 secondary indexes are the focus of coal-mine water-hazard risk prevention and control, among which seven indexes are the primary starting point for coal-mine water-hazard risk prevention and control. The groundwater index in particular has the most prominent impact. These results can provide a theoretical basis and scientific guidance for the specific water-hazard prevention and control work of coal mines.

Compensation Mechanism for Ecological Diversity Governance in Chinese River Basins Application Based on Low-Carbon Water Quality Game Theory

Background: Taking the construction of ecological civilization as an important core of the overall layout of the “Five in One” and the coordinated promotion of the “Four Comprehensives” strategic layout, combined with the global concept of ecological environment governance, provides a new direction for the reform and innovation of China’s watershed ecological compensation system through diversified governance. Subjects and methods: This article focuses on ecological compensation in river basins, exploring collaborative cooperation models between upstream and downstream of the basin under the dual constraints of “low-carbon” and “water quality”, to achieve a “win-win” situation between the ecological environment of the basin and all parties involved in basin protection. Based on the theory of evolutionary game theory, the indicators of “carbon emissions” and “water quality” are introduced to construct a diversified ecological co-governance compensation strategy model for the watershed. By exploring the optimal strategies among various entities in the upstream and downstream of the watershed. Results: (1) In the initial stage, the optimal strategy for ecological compensation in the watershed among stakeholders cannot achieve a stable balance through their evolution; (2) In the mature stage, based on the regulation of the superior government, interest subjects will choose a mutual supervision strategy to avoid bearing high penalties, to achieve Pareto effectiveness in achieving a stable overall economy of the basin; (3) By paying for high-quality resources from downstream and implementing carbon trading among basin entities, we can promote internal resource digestion, reduce intermediate transaction costs, and deeply promote the overall green and sustainable development of the basin. Through analysis, it has been proven that the conclusion is effective, providing decision support for the diversified co-governance of watershed ecosystems. Based on building an ecological community with a shared future in the watershed, we aim to achieve the construction of a community with a shared future for mankind.

Evolution strategies for collaborative governance of marine microplastic pollution from the industry-research integration perspective

IntroductionMarine microplastics, are widely distributed in the global marine environment, posing a challenging issue that requires the joint efforts of global stakeholders.MethodsTo effectively address the issue of marine microplastic pollution (MMP) governance and analyze the dynamic changes in governance willingness of various participants under different scenarios, this paper meticulously constructs a game theory framework encompassing polluting enterprises, research institutions, and environmental organizations. Results(1) On the political level, the implementation of continuous and strong economic penalty mechanisms is an effective means to deter enterprises from evading MMP governance responsibilities. However, the effective execution of this strategy highly depends on the participation and supervision of environmental organizations. Therefore, it is essential to assign more roles and responsibilities to environmental organizations to ensure the thorough execution of governance measures. (2) On the technical level, the effectiveness of research directly determines the functional status of enterprises and research institutions in the MMP governance decision-making system. Weaker entities tend to make decisions following the behavioral preferences of dominant entities. Thus, deepening the integration of industry and research and fully unleashing the effectiveness of research outcomes in MMP governance is a key path to enhancing overall governance efficiency and effectiveness. (3) On the economic level, high governance costs often become a significant factor limiting the enthusiasm of all parties to participate. However, when innovative cooperation models achieve cost sharing and benefit sharing, the governance willingness of participants significantly increases. It is evident that optimizing resource allocation, improving the efficiency of fund utilization, and establishing a diversified and sustainable funding guarantee mechanism are crucial for advancing the in-depth progress of MMP governance. DiscussionIn summary, this study not only provides profound theoretical insights into the interaction relationships and behavioral choices of multiple stakeholders in MMP governance but also offers practical strategic recommendations for constructing an efficient and collaborative governance system.

Empirical evidence of resource dependent evolution of payoff matrices in Saccharomyces cerevisiae populations.

In evolutionary game theory, a relative comparison of the cost and benefit associated with obtaining a resource, called payoff, is used as an indicator of fitness of an organism. Payoffs of different strategies, quantitatively represented as payoff matrices, are used to understand complex inter-species and intra-species interactions like cooperation, mutualism, and altruism. Payoff matrices, however, are usually treated as invariant with time - largely due to the absence of any empirical data quantifying their evolution. In this paper, we present empirical evidence of three types of resource-dependent changes in the payoff matrices of evolving Saccharomyces cerevisiae populations. We show that depending on the carbon source and participating genotypes, N-player games could collapse, be born, or be maintained. Our results highlight the need to consider the dynamic nature of payoff matrices while making even short-term predictions about population interactions and dynamics.

Research on the diffusion and control of unsafe behaviors among chemical industry park enterprises based on the SEIR evolutionary game model

In order to control the diffusion of unsafe behaviors among chemical industrial park enterprises, a Susceptible-Exposed-Infectious-Recovered (SEIR) evolutionary game model is constructed based on the theory of epidemiology and evolutionary game theory. By exploring the game relationship between emergency management departments and safety assessment agencies, the paper analyzes the diffusion paths and evolutionary patterns of unsafe behaviors in chemical industrial park enterprises under different behavioral strategies adopted by both parties. Furthermore, it examines the process and patterns of system evolution to a positive stable state, and conducts multi-scenario simulation and analysis. The results indicate that the interactive behaviors of "strict regulation" by emergency management departments and "high-quality safety assessment" by safety assessment agencies are more conducive to controlling the diffusion of unsafe behaviors among chemical industrial park enterprises. Improving the efficiency of emergency management departments, establishing an attractive and constraining reward and punishment system to guide safety assessment agencies in conducting high-quality safety assessments, and stimulating the initiative of chemical industrial park enterprises in safety behaviors will be more conducive to forming an integrated, coordinated, and mutually constraining mechanism for work safety governance.

Identification of optimal waste-to-energy strategies for sustainable development in Iran: SWOT analysis, hybrid MCDM methods, and game theory

The growing global focus on environmental sustainability and the pressing need for efficient waste management and energy crisis mitigation have prompted extensive investigations into sustainable waste management strategies. Given Iran's economic development and population growth, the country faces challenges in energy supply and waste management, making waste-to-energy (WtE) applications a promising solution for sustainable waste management. This study employs a combination of SWOT (Strengths, Weaknesses, Opportunities, and Threats) analysis, Multi-Criteria Decision-Making (MCDM) approaches, and game theory to explore WtE technologies and processes, evaluate their applicability within Iran's context, and identify the most effective WtE strategies for the country. Furthermore, game theory and fuzzy Shapley value analysis were utilized to determine the optimal combination of WtE development strategies. The strategy player “SO” held the highest position of power, with a fuzzy Shapley value of (0.391, 1.744, 3.264), resulting in the identification of the optimal strategy combination of SO2ST2WO1WT2, with a value of (0.429, 0.679, 0.893). The recommended combination emphasizes landfill with gas capture, development of incineration power plants, and integrated resource recovery through residue-derived fuel (RDF) implementation. Achieving these objectives necessitates energy policy reforms, pricing adjustments, improvements in the energy subsidy system, and infrastructure and market development.

GTDI: a game-theory-based integrated drought index implying hazard-causing and hazard-bearing impact change

Abstract. Developing an effective and reliable integrated drought index is crucial for tracking and identifying droughts. The study employs game theory to create a spatially variable weight drought index (game-theory-based drought index, GTDI) by combining two single-type indices: an agricultural drought index (standardized soil moisture index, SSMI), which implies drought hazard-bearing conditions, and a meteorological drought index (standardized precipitation evapotranspiration index, SPEI), which implies drought hazard-causing conditions. In addition, the entropy-theory-based drought index (ETDI) is introduced to incorporate a spatial comparison with GTDI to illustrate the rationality of gaming weight integration, as both entropy theory and game theory belong to linear combination methods in the development of the integrated drought index and entropy theory has been applied in related research. Leaf area index (LAI) data are employed to confirm the reliability of GTDI in identifying drought by comparing it with SPEI, SSMI, and ETDI. Furthermore, a comparative analysis is conducted on the temporal trajectories and spatial evolution of the GTDI-identified drought to discuss GTDI's level of advancement in monitoring changes in hazard-causing and hazard-bearing impacts. The results show that GTDI has a very high correlation with single-type drought indices (SPEI and SSMI), and its gaming weight integration is more logical and trustworthy than that of ETDI. As a result, it outperforms ETDI, SPEI, and SSMI in recognizing drought spatiotemporally and is projected to replace single-type drought indices to provide a more accurate picture of actual drought. Additionally, GTDI exhibits the gaming feature, indicating a distinct benefit in monitoring changes in hazard-causing and hazard-bearing impacts. The case studies show that drought events in the Wei River basin are dominated by a lack of precipitation. The hazard-causing index, SPEI, dominates the early stages of a drought event, whereas the hazard-bearing index, SSMI, dominates the later stages. This study surely serves as a helpful reference for the development of integrated drought indices as well as regional drought prevention and monitoring.

Evaluation of Urban Public Building Renovation Potential Based on Combination Weight Cloud Model—Case Study in China

Currently, urban renovation activities in China are booming. And promoting the renovation of public buildings is a key feature of urban renovation due to its large scale, high cost, and significant impact to the natural and social environment. To reduce the ambiguity and uncertainty in evaluating the potential for the renovation of existing public buildings, a renovation potential evaluation model integrating a game theory-based combination weighting method and cloud model theory is proposed. This paper constructs a comprehensive evaluation index system based on relevant standards and the literature. Game theory is used to optimize the weights obtained by AHP and entropy weight methods to obtain a combined weight. MATLAB programming is used to calculate the comprehensive cloud parameters of the evaluation index for the potential renovation of existing public buildings and therefore generate cloud Graphs. Through a case study in Nanjing, China, it was demonstrated that the combination weight cloud model can objectively reflect the relationship between the fuzziness and randomness of evaluation indicators for public building renovation potential. The visual expression of cloud Graphs can intuitively reflect the magnitude of renovation and renovation potential and the degree of uncertainty in evaluation results. The research result provides useful references for the sustainable utilization of building resources in the era of building.

A game-based power system planning approach considering real options and coordination of all types of participants

With the ongoing advancement of global power marketization, the increasing diversity of stakeholders in the power market and their interactions have a significant impact on power system planning and operation. Traditional methods employ game theory to describe the interactions among market participants. However, these approaches fail to include all relevant participant types and overlook the long-term uncertainty value of planning schemes. Therefore, this paper proposes a game theory-based power system planning approach considering real options (RO) and coordination of all types of participants. First, the dynamic gaming interaction among supply-transmission-demand is studied, and the independent system operator is integrated into the game planning framework based on the overall perspective of power market operation. Moreover, the new power supply, grid planning, and operation of distributed generation (DG) are taken as decision variables based on the RO theory, and a game decision model of all participants in the power system planning considering the investment uncertainty is constructed. Finally, the iterative search algorithm is employed to solve the model, and the framework is validated based on the IEEE 30-bus system. The results indicate that through collaborative planning involving various market participants, Generation Companies and Transmission Companies expand their investments to maximize profits, while large power consumers reduce their investment in DG and instead increase their direct power purchases to lower costs. Moreover, these participants are inclined to pursue projects with higher asset value volatility, which further enhances their profit. By integrating RO theory with game theory, the proposed approach establishes a comprehensive planning framework that effectively addresses investment uncertainty. This integration enables market participants to make more optimal decisions, ultimately leading to an enhancement in the long-term economic performance of the power system.

Whether higher risk indicates severe loss in the flood disaster assessment: A comparative analysis in the Hubei province of central China

Study regionHubei province, Yangtze River Basin, Central China Study focusRisk and loss analysis constitutes a critical element of flood disaster management. Nevertheless, the relationship between risk and loss has been infrequently examined in the literature. Here we developed a comparative analysis framework for assessing flood risk and loss in Hubei Province. The risk model incorporates 22 indicators in terms of hazard, exposure, vulnerability and emergency response & recovery capability. Indicator weights were determined through a combination of objective and subjective weighting methods based on the game theory. Flood risk and loss levels were classified using fuzzy comprehensive evaluation and grey correlation analysis respectively. New hydrological insightsAnnual risk and loss maps exhibit a spatial pattern of higher levels in the eastern regions and lower levels in the western regions. However, the relationship between risk and loss was not as well as expected during designated flood periods. While regions impacted by disasters typically demonstrated higher risk levels, the risk in the regions unaffected by flood disasters appeared to be overestimated. By analyzing flood risk and loss across various temporal scales, this research contributes a novel perspective for the evaluation of flood risk models.

Optimizing integrated energy systems at park level: A cooperative game approach with exergy economics

This study presents a comprehensive framework for optimizing energy systems by integrating exergy analysis, energy economics, and game theory. The concept of exergy, which quantifies the usable energy within a system, is employed to evaluate energy efficiency and losses across various energy sources, including thermal, cooling, chemical, and electrical systems. Stoichiometric coefficients, denoted by the factor λ, are utilized to simplify exergy calculations for different energy types and processes. The economic evaluation of energy flows is conducted through energy economics principles, incorporating cost allocation and balance equations. The integration of game theory into the optimization model ensures strategic interactions among energy components, leading to a Nash equilibrium that balances economic performance, efficiency, and environmental sustainability. The model also accounts for emissions and the required proportion of renewable energy. To solve the complex optimization problem, a modified Particle Swarm Optimization (PSO) algorithm is employed, featuring adaptive mechanisms for velocity and inertia updates, enhancing the search process for the optimal solution. The proposed framework is designed to optimize the Integrated Energy System (IES) efficiently, ensuring sustainable and economically viable energy management. The analysis of optimization strategies highlights a trade-off between cost and efficiency. Strategy 1, focused on minimizing cost, achieves the lowest cost at 4069.37 CNY, 25.79 % less than Strategy 2, but with a reduced exergy efficiency of 59.82 %, which is 10.14 % lower than Strategy 2′s 68.47 %. Strategy 3 offers a balanced approach, with a cost of 4970.89 CNY, 9.43 % higher than Strategy 1 but 9.43 % lower than Strategy 2. It achieves an exergy efficiency of 67.87 %, only 0.60 % lower than Strategy 2, thus providing a practical compromise between economic performance and efficiency.

Game theoretic operation optimization of photovoltaic storage charging station considering uncertainty and carbon trading

With the advancement of energy conservation and emission reduction efforts, the orderly charging of electric vehicles and the operation of photovoltaic-storage-charging stations associated with electric vehicles have become increasingly important topics. This study constructs an optimization model for the operation of stations under the synergy of electricity and carbon markets from a game theory perspective. Firstly, Latin hypercube sampling and Monte Carlo sampling are employed to handle the uncertainties in photovoltaic output and the stochastic nature of electric vehicles charging. Secondly, a ladder-type carbon trading mechanism is introduced, and a charging optimization model based on Stackelberg game theory is developed to describe the benefit interaction between charging stations and electric vehicles users. In this model, the upper level represents the charging station operator aiming to maximize joint electricity and carbon revenue while minimizing load fluctuations, whereas the lower level represents electric vehicles users aiming to maximize consumer surplus. Finally, a genetic algorithm nested with mixed-integer linear programming is used to solve the optimization model. The simulation results validate the model's effectiveness and superiority. The results indicate that, compared to centralized optimization methods, the Stackelberg game mechanism can increase consumer surplus by 119.40 %, reduce carbon emissions by 217.92 %, and achieve a win-win situation for both parties. Compared to a fixed carbon trading value, the ladder-type carbon trading mechanism can reduce carbon emissions by 23.84 % and smooth load fluctuations.