Game Model Research Articles

Public participation in Governance of E-waste recycling: A tripartite evolutionary game analysis

The surge in informal E-waste recycling has led to significant resource wastage and environmental hazards. The current government-centered governance system faces substantial obstacles to effective implementation due to information gaps and operational challenges. This study adopts the concept of social governance by incorporating public participation into the traditional government-led e-waste recycling system. Utilizing the bounded rationality of evolutionary game theory, this research constructs a tripartite game model involving the government, recyclers, and the public. It analyzes the behavioral strategy choices of each participant and the mechanisms of mutual influence under different scenarios. The main findings are: (1) Solely relying on public power is insufficient for effectively governing informal recyclers. (2) Reasonable and moderate incentives can promote public participation, serving as an effective supplementary tool for government regulation. (3) Increasing public exposure to the informal dismantling behaviors of recyclers is crucial for enhancing governance effectiveness. Specific measures can include establishing complaint departments for related incidents and creating media channels. These findings underscore the importance of integrating public participation into e-waste governance to address the limitations of a purely government-centered approach.

Spontaneous Formation of Evolutionary Game Strategies for Long-Term Carbon Emission Reduction Based on Low-Carbon Trading Mechanism

In the context of increasing global efforts to mitigate climate change, effective carbon emission reduction is a pressing issue. Governments and power companies are key stakeholders in implementing low-carbon strategies, but their interactions require careful management to ensure optimal outcomes for both economic development and environmental protection. This paper addresses this real-world challenge by utilizing evolutionary game theory (EGT) to model the strategic interactions between these stakeholders under a low-carbon trading mechanism. Unlike classical game theory, which assumes complete rationality and perfect information, EGT allows for bounded rationality and learning over time, making it particularly suitable for modeling long-term interactions in complex systems like carbon markets. This study builds an evolutionary game model between the government and power companies to explore how different strategies in carbon emission reduction evolve over time. Using payoff matrices and replicator dynamics equations, we determine the evolutionarily stable equilibrium (ESE) points and analyze their stability through dynamic simulations. The findings show that in the absence of a third-party regulator, neither party achieves an ideal ESE. To address this, a third-party regulatory body is introduced into the model, leading to the formulation of a tripartite evolutionary game. The results highlight the importance of regulatory oversight in achieving stable and optimal low-carbon strategies. This paper offers practical policy recommendations based on the simulation outcomes, providing a robust theoretical framework for government intervention in carbon markets and guiding enterprises towards sustainable practices.

Effects of conservative-militant defection strategies on the evolution of cooperation in social dilemma

Competition in the international arena and business realm offers avenues for individual growth and advancement. Individuals using different means of competition can obtain unequal rewards. This paper claims that when no consensus is reached in business activities, defectors will choose conservative or militant defection strategies during market competition. Conservative defectors, who are in a comparatively weak position, need to pay the costs brought by market share losses. However, their personal abilities cannot be ignored, which prompts them to bravely choose the conservative defection strategy. This brings rewards to conservative defectors. Militant defectors, typically in stronger positions, also receive greater rewards. Research results establish an evolutionary game model of three strategies, the cooperation strategy, the conservative defection strategy, and the militant defection strategy. After the system is stable, this model displays two stable states. Through numerical simulation, it can be found that the personal abilities of conservative defectors play a decisive role in promoting cooperation. However, the market share losses of conservative defectors have periodical impacts on cooperation. Moreover, the threats of militant defectors to cooperation should be comprehensively considered in combination with the personal abilities of conservative defectors.

Evolutionary game analysis of multi-agent cooperation strategy analysis in agricultural water conservancy PPP project under digitization background

This study constructed a system dynamics (SD) evolutionary game model, from which we analyzed the conditions that need to be met by multi-agents to achieve cooperation in agricultural water conservancy (AWC) Public-Private Partnership (PPP) projects. Simultaneously, this study used numerical simulation to depict the impact of initial participation willingness, reward, punishment, income, and other parameters of local governments, project enterprises, and farmers on the evolution strategy. The results firstly showed that the basic conditions for tripartite cooperation are to strengthen the rewards and punishments for project enterprises and improve the participation benefits of farmers. Secondly, it showed that increasing the rewards for farmers and improving the project dividend benefits can effectively motivate farmers to participate. Thirdly, it showed that enhancing the incentive subsidies and reputation benefits for project enterprise’s participation, as well as strengthening the supervision of local government, boosts the motivation of project enterprises significantly. However, it is vital to ensure that the reward amounts are not too high to allow local government to play its guiding role efficiently. Lastly, the results indicated that digital technology can help reduce the participation cost of local government, project enterprises and farmers, and improve the external reputation benefits of each participant, thus forming a win-win situation for all three participants. Analyzing the cooperation strategies of the three parties in AWC PPP projects provides theoretical support and a decision-making basis for the efficient operation of AWC PPP projects under the digital background, and also provides practical policy recommendations for the high-quality development of AWC.

DEVELOPMENT PROCESS OF THREE-DIMENSIONAL CHARACTER DESIGN AND MODELING FOR MOBILE GAMES

This research focuses on the development process of three-dimensional character design and modeling in mobile games with the rapid development of the game market in the world and in Turkey. The rapid development of the game market has led to an increase in the number of these companies and the necessity to create, develop and improve the infrastructure of the games by programming mobile games and adding new design elements with the increasing number of companies invested or acquired by important national or international companies. Undoubtedly, the visuality used in games is very important in terms of increasing the demand for them and the pleasure they will give to the player. Especially three-dimensional character design ranks first among the criteria that increase the appreciation of the game. Characters should be well designed and original in order to be adopted and preferred by users. This study aims to reveal the development process of three-dimensional character design for mobile games. With this research, it is aimed to draw attention to the design and modeling stages of three-dimensional characters produced for mobile games. The data obtained as a result of the research on the subject show that character design, which is one of the design steps that determine the success of a game, has important contributions from the development stage of the game to the marketing stage. The effectiveness of the character reinforces the bond that the users establish with him/her and thus enables them to internalise and adopt the game they play. For this reason, it has been determined that while character design is critical to the success of a game, it should also be considered that it includes various other elements that also affect the overall game experience.

Cocreation of social value: A tripartite game analysis with Chinese state-owned enterprises as an example.

In the context of the digital economy era, it is urgent for Chinese state-owned enterprises (SOEs) to engage in social value cocreation activities. The government and consumers' roles in SOEs' social value cocreation system cannot be ignored. Therefore, it is necessary to explore the tripartite social value cocreation model involving the government, SOEs, and consumers. In this respect, this study constructs a tripartite evolutionary game model of the government, SOEs, and consumers, and explores the influencing factors and evolutionary mechanism of the system overall. Matlab software is used to analyze the simulation data. The results reveal that the prerequisite for SOEs' successful social value cocreation is that consumers receive additional social value benefits greater than the level of improvement in social welfare. The allocation coefficient of consumers' additional social value benefits, the degree of the government's digital empowerment subsidy, and the level of the punishment for SOEs that violate the government's cocreation requirements will accelerate the achievement of equilibrium in the social value cocreation system, without affecting the final equilibrium result. By analyzing the strategic choices and interactive relationships among the government, SOEs, and consumers in social value cocreation in-depth, this study offers suggestions to promote the government, SOEs, and consumers' participation in social value cocreation. This research contributes to clarifying SOEs' social value cocreation model and has significant implications for promoting enterprises' high-quality development.

The impact of time delays on mutant fixation in pairwise social dilemma games

Evolutionary game theory examines how strategies spread and persist in populations through reproduction and imitation based on their fitness. Traditionally, models assume instantaneous dynamics where fitness depends on the current population state. However, some real-world processes unfold over time, with outcomes emerging from history. This motivates incorporating time delays into evolutionary game models, where fitness relies on the past. We study the impact of time delays on mutant fixation in a Moran Birth–death process with two strategies in a well-mixed population. At each time step of the process, an individual reproduces proportionally to fitness coming from the past. We model this as an absorbing Markov chain, allowing computational calculation of the fixation probability and time. We focus on three important games: the Stag-Hunt, Snowdrift and Prisoner’s Dilemma. We will show time delays reduce the fixation probability in the Stag-Hunt and the Prisoner’s Dilemma but increase it in the Snowdrift. For the Stag-Hunt and the Prisoner’s Dilemma, time delays lengthen the fixation time until a critical point, then reduce it. The Snowdrift exhibits the opposite trend.

Optimal operation of multi-energy microgrids with shared energy storage clusters by master-slave games

Abstract As shared energy storage power plants have become a research hotspot, the cooperation between them and microgrids has attracted attention. In this paper, we propose a master-slave game optimization operation strategy for multi-energy microgrids, taking into account shared energy storage (ESS) clusters. Firstly, the inclusion of ESS clusters is considered in a combined heat and power (CHP) type multi-energy microgrid. Then, the optimal operation model is established and solved in two layers. The master-slave game model in the context of ESS clusters is proposed by analyzing the game relationship between the microgrid side and the user side, the arithmetic simulation with MATLAB, and the modeling and solving are carried out by the Yalmip tool and the CPLEX solver, and the combination of heuristic algorithms and the solver is used to optimize the strategies of the microgrid side and the user side. The optimization of the system after the optimization of this paper’s methodology can enhance the system economy.

Heterogeneously Networked Evolutionary Games With Intergroup Conflicts.

Network games primarily explore the intricacies of individual interactions and adaptive strategies within a network. Building upon this framework, the present study delves into the modeling, analysis, and control of heterogeneously networked evolutionary games with intergroup conflict (HNEG-IC), where attacking players possess area-monitoring capabilities with limited attacking power. To begin with, a mathematical model is introduced to capture intragroup strategy dynamics and intergroup conflicts of HNEGs-IC via the algebraic state space representation (ASSR). A necessary and sufficient condition for achieving global cooperation of HNEGs-IC is established. Then, a criterion for verifying the κ -cooperation below a certain mortality is presented. Considering the HNEGs-IC with strategy feedback control, it is proven that the feedback control, subject to global cooperation, is robust to conflicts when the intersection of the strategy threshold set and the reachable set of the preset initial strategy profiles is empty. Finally, for verification and demonstration, the obtained results are applied to a simplified virtual game model of the NATO and the Warsaw Pact.

Carbon emission reduction dynamic decision-making in the electricity supply chain with different carbon emission allowance principles

To address the impacts of typical principles for allocating initial carbon emission allowance, namely, the grandfathering and benchmarking principles on long-term emission reduction strategies, this paper presents four differential game models for an electricity supply chain consisting of a single electricity supplier and a single electricity retailer. The equilibrium solutions for different models are obtained and comparatively analyzed. The results show that the power supplier exhibits greater emission reduction efforts and, therefore, that the retailer has higher profits under the benchmarking principle than under the grandfathering principle. Moreover, under the two principles, the level of the power supplier’s emission reduction efforts is related to the decision-making modes of the electricity supply chain. Under specific conditions, the power supplier’s profit is also higher under the benchmarking principle than under the grandfathering principle. In addition, this study extends the models to investigate the constrained differential game models and obtains the game equilibrium solutions, which can be proved as saddle point equilibria.

Iterative algorithms for solving one-sided partially observable stochastic shortest path games

Real-world scenarios often involve dynamic interactions among competing agents, where decisions are made considering actions taken by others. These situations can be modeled as partially observable stochastic games (POSGs), with zero-sum variants capturing strictly competitive interactions (e.g., security scenarios). While such models address a broad range of problems, they commonly focus on infinite-horizon scenarios with discounted-sum objectives. Using the discounted-sum objective, however, can lead to suboptimal solutions in cases where the length of the interaction does not directly affect the gained rewards of the players.We thus focus on games with undiscounted objective and an indefinite horizon where every realization of the game is guaranteed to terminate after some unspecified number of turns. To manage the computational complexity of solving POSGs in general, we restrict to games with one-sided partial observability where only one player has imperfect information while their opponent is provided with full information about the current situation. We introduce two novel algorithms based on the heuristic search value iteration (HSVI) algorithm that iteratively solve sequences of easier-to-solve approximations of the game using fundamentally different approaches for constructing the sequences: (1) in GoalHorizon, the game approximations are based on a limited number of turns in which players can change their actions, (2) in GoalDiscount, the game approximations are constructed using an increasing discount factor. We provide theoretical qualitative guarantees for algorithms, and we also experimentally demonstrate that these algorithms are able to find near-optimal solutions on pursuit-evasion games and a game modeling privilege escalation problem from computer security.

Optimal financing strategies for low‐carbon supply chains: A Stackelberg game perspective

AbstractThis study constructs a Stackelberg game model between low‐carbon manufacturers and capital‐constrained retailers. Considering the manufacturer's financing model, the manufacturer's investment model, and the internal blended financing model, it studies the optimal wholesale price of manufacturers. This paper investigates the impact of consumers' low‐carbon preference, the financing interest rate of manufacturers, investment ratio, investment return on carbon emission reduction investment, and supply chain pricing. The conditions for low‐carbon supply chain participants to choose the best financing mode and the impact of different financing models on the performance of low‐carbon supply chains were obtained.

When multi-group selection meets mystery of cooperation in structured public goods games.

Cooperation is the cornerstone of social stability and human development. In order to promote mutual cooperation among individuals, some researchers analyzed the important factors influencing individual behavior from the perspective of group selection, while others revealed the evolutionary mechanism of cooperative behavior in groups from the perspective of network reciprocity. However, group selection and network reciprocity actually work together and simultaneously drive individuals to cooperate with each other. Analyzing each mechanism in isolation provides an incomplete understanding of the interaction process. Inspired by this, we integrate the coupled effects of both group selection and network reciprocity on the behavior of individuals. We develop a structured public goods game model to study the evolution of individual cooperative behavior in multiple groups, where each individual can interact not only with intra-group individuals but also with inter-group individuals. Based on the fixed probabilities of multi-group selection, including intra-group and inter-group selection, we derive a general condition that promotes cooperation among individuals. Besides, we discuss the effects of the number of neighbors in a group, group size, and group size on the selection of cooperative behavior. Finally, we systematically compare our model with the well-mixed case, and the results show that a structured population enhances cooperation. Increasing the number of populations boosts the fixation probability of cooperation. To the best of our knowledge, this paper is the first to study the cooperative evolutionary dynamics of multi-group selection in structured populations through public goods games.

How to subsidize ecotourism in a tourism supply chain? An examination with a three-party evolutionary game model

Nowadays, to promote ecotourism, governments have introduced a series of incentive policies. This study considers the impacts of government subsidy on ecotourism development and builds a three-party evolutionary game model involving the government, tourism enterprises and downstream consumers. The game strategies and behavior evolution of each party have been studied. Three conditional evolutionarily stable strategy points are obtained. The authors also investigate the final evolutionary results, influencing factors and optimization paths of various parties. Some interesting conclusions are drawn. First, in the introduction stage of ecotourism, government subsidies are effective at boosting ecotourism. However, when the market reaches stabilization, enterprises and consumers might not choose ecotourism even with government subsidies. Second, during the evolutionary process, the government subsidies probability exhibits two trends of an initial increase followed by a subsequent fall to zero, or ongoing subsidies. Finally, the initial state of the government, enterprises and consumers has a greater impact on the stability outcomes. When enterprises' and consumers' initial preferences for ecotourism grow, the government's willingness to subsidize diminishes significantly. Meanwhile, subsidies for consumers work better than those for enterprises.

A Robust Mean-Field Actor-Critic Reinforcement Learning Against Adversarial Perturbations on Agent States.

Multiagent deep reinforcement learning (DRL) makes optimal decisions dependent on system states observed by agents, but any uncertainty on the observations may mislead agents to take wrong actions. The mean-field actor-critic (MFAC) reinforcement learning is well-known in the multiagent field since it can effectively handle a scalability problem. However, it is sensitive to state perturbations that can significantly degrade the team rewards. This work proposes a Robust MFAC (RoMFAC) reinforcement learning that has two innovations: 1) a new objective function of training actors, composed of a policy gradient function that is related to the expected cumulative discount reward on sampled clean states and an action loss function that represents the difference between actions taken on clean and adversarial states and 2) a repetitive regularization of the action loss, ensuring the trained actors to obtain excellent performance. Furthermore, this work proposes a game model named a state-adversarial stochastic game (SASG). Despite the Nash equilibrium of SASG may not exist, adversarial perturbations to states in the RoMFAC are proven to be defensible based on SASG. Experimental results show that RoMFAC is robust against adversarial perturbations while maintaining its competitive performance in environments without perturbations.

An approach to formalization of WEEE informal collectors: Collection model under a membership-based community

Informal collectors’ formalization has become a key challenge that developing countries such as China face in governing informal recycling. This study establishes an innovative collection model of waste electrical and electronic equipment (WEEE) under the membership community operation system, which integrates waste merchants into the formal recycling system in the form of members. Based on a Bass model of membership community development and an evolutionary game model between recyclers and waste merchants, respectively, this study uses system dynamics theory to simulate and analyze the model’s implementation effectiveness and influencing factors. We find that the membership community’s interpersonal promotion and customer relationship management strategies can increase waste merchants’ membership rate and membership loyalty, which is an effective way to incorporate waste merchants into the formal recycling system. Waste merchants’ main interest demands in the formalization process are to gain economic benefits and identity recognition, which motivate them to become members. Membership’s transaction cost establishes a long-term cooperative relationship between waste merchants and recyclers in the form of an economic contract. However, the potential losses from information sharing are the key factor restricting waste merchants from enrolling as members, which has also become the main obstacle to their formalization. This study provides a new theoretical and empirical basis for informal collectors’ formalization, which has important practical significance for WEEE recycling and management in developing countries.

Research on the mechanism of human-machine security collaboration of miners considering automation trust

Safety in the coal mining industry is a long-standing issue. With the implementation of intelligent construction in coal mines, humans–machine collaboration is critical to accident prevention. We investigate the psychological dynamics among miners during intelligent construction by developing distinct evolutionary game models for miner security collaboration mechanisms, while also considering the level of trust in automation. We explore the impact of changes in automation trust on the human–machine security collaboration behaviour among miners as well as the regulatory strategies adopted by coal mining enterprises. Evidently, the current level of automation trust among miners is insufficient to ensure safety, and the safety management systems of coal mining enterprises are yet to reach a stable state. Examination of the relevant parameters using specific examples reveals that the optimal range for the level of automation trust among miners lies between 0.7 and 0.9, indicating a favourable coal mine safety production system. These conclusions provide a scientific foundation for effectively enhancing safety management in the context of intelligent construction in coal mines.

Navigating the energy transition with the Carbon-Energy-Green-Electricity scheme: An industrial chain-based approach for China's carbon neutrality

In exploring the intricate dynamics of China's energy transition towards a national certificate trading market, this study harnesses a two-stage game model to unravel the nuanced decision-making within the intertwined carbon emissions trading, energy-consumption permit trading, and electricity markets. A novel industrial chain-based policy framework, i.e., the Carbon-Energy-Green-Electricity (CEGE) scheme, is introduced to address the complexity inherent in aligning these trading markets towards carbon neutrality goals. Findings reveal that the current isolated energy transition policies lead to increased electricity prices and imposes redundant regulatory burdens on power companies. By advocating for the CEGE scheme, the study presents a strategic approach to alleviate these challenges, highlighting its potential to lower electricity costs and foster more efficient carbon reduction efforts. Furthermore, it underscores the importance of integrating energy transition policies, including CET, ECPTS, the renewable portfolio standards (RPS), and the tradable green certificate program (TGC), to enhance renewable energy adoption, offering a path to relieve financial pressures on households while supporting broader environmental and economic welfare improvements.

Optimal strategies for virtual power plants to participate in medium- and long-term power trading in the context of contracts for difference (CFDs)

Abstract In the context of virtual power plants gradually joining the medium-and long-term power market transactions, the decision-making problem of this new subject in the transaction process has attracted wide attention. Since virtual power plants possess distributed power sources on the supply side, as well as variable loads, energy storage, and other resources on the customer side, they are able to participate in both the sale and purchase of electricity in the medium-and long-term electricity market at the same time, which leads to the need for the relevant analysis to be divided into the two cases of sale and purchase of electricity. At the same time, due to the wide application of the CFD mechanism, power transactions should also take into account the compensation adjustment brought by this mechanism in addition to the market price. To sum up, this paper constructs a static game model for the virtual power plant’s power sales and purchasing strategies in the medium-and long-term power market under the premise of the CFD mechanism. The analysis shows that the optimal trading volume is related to the CFD volume, the total volume of power supplied by the bidding, the market price, etc. The relevant conclusions will help market managers to grasp the market price. The conclusions of the analysis help market managers grasp the key transaction information and assist virtual power plants to participate in medium-and long-term power transactions in an orderly manner.

Competitive Supply Chain Strategy Optimization Based on Game Model and NSGA-II Algorithm

Competitive Supply Chain Strategy Optimization Based on Game Model and NSGA-II Algorithm