Evolutionary Equilibrium Research Articles

Formalizing the law of diminishing returns in metabolic networks using an electrical analogy.

The way biological systems respond to changes in parameter values caused by mutations is a key issue in evolution and quantitative genetics, as it affects fundamental aspects such as adaptation, selective neutrality, robustness, optimality, evolutionary equilibria, etc. We address this question using the enzyme-flux relationship in a metabolic network as a model of the genotype-phenotype relationship. The lack of a suitable mathematical tool from biochemical theory to investigate this relationship led us to use an analogy between electrical circuits and metabolic networks with uni-uni reactions. We show that a behaviour of diminishing returns, which is commonly observed at various phenotypic levels, is inevitable, irrespective of the complexity of the system. We also present a possible generalization to metabolic networks with both uni-uni and bi-bi reactions.

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

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

Research and application of a novel graph convolutional RVFL and evolutionary equilibrium optimizer algorithm considering spatial factors in ultra-short-term solar power prediction

With the increasing proportion of photovoltaic power generation, solar power prediction systems have become more important. Accurate photovoltaic power prediction can assist the grid dispatch department in formulating effective power scheduling plans, improving grid stability and the capacity to accommodate solar energy. To address the challenges in solar power generation forecasting, the paper proposes a new neural network model called Graph Convolutional Random Vector Functional Link (GCRVFL). The output layer of this model includes both nonlinear transformed features from the hidden layer and the original input features, while also considering the spatial characteristics among photovoltaic sites. Furthermore, Singular Spectrum Analysis (SSA) is utilized to decompose the original solar power time series, extracting different component sequences from the photovoltaic power time series. Opposite based learning and cross-mutation are employed to improve the original Equilibrium Optimizer (EO) algorithm, resulting in an Evolutionary Equilibrium Optimizer (EEO) algorithm. The EEO algorithm is employed to optimize the weight threshold of GCRVFL, leading to a novel photovoltaic power prediction model called SSA-EEO-GCRVFL. Through four datasets and eight control experiments, it can be observed that the proposed model achieves the best predictive performance and is capable of fulfilling the task of photovoltaic power prediction.

Synergizing stakeholder collaboration for value co-creation in China's prefabricated decoration diffusion: A tripartite evolutionary game perspective

The emerging prefabricated decoration (PD) sector in China offers a compelling avenue for revolutionizing the construction industry, aligning with the imperatives of sustainability and industrialization. However, the outlook for the diffusion of PD in China's construction industry is less than promising. The development of PD is closely related to its value creation and the intricate interplay of stakeholder strategies and their ramifications on PD's value co-creation necessitates thorough exploration. Based on evolutionary game theory, this study elucidates the dynamic interactions among local governments, developers, and decoration contractors in China's evolving PD landscape. A tripartite evolutionary game model was established, investigating the evolutionary stable equilibriums and the corresponding strategies. Then, an empirical analysis in Chongqing City validates the game models and primary conclusions. Scrutinizing subsidy thresholds, local subsidy biases, PD proportion in prefabrication, and binary innovation allocation, the research unveils nuanced insights pertinent to boosting PD's value co-creation. Findings advocate an assembly rate threshold of subsidy (65%–70 %) and a shift towards incentivizing decoration contractors to catalyze PD adoption. Additionally, excessive PD proportion and immature product investments may hinder industry development, prompting stakeholders to recalibrate strategies dynamically. These findings characterize the mechanisms of stakeholder value co-creation during the PD diffusion, enriching the implications of value co-creation theory in the emerging industry of the construction sector. They also furnish stakeholders committed to promoting the diffusion of PD in the domestic and international construction sectors with practical strategic guidance, particularly tailored for cities in the early stages of PD development.

Game analysis on PPP model operation of abandoned mines ecological restoration under the innovation of central government's reward and punishment system in China.

There is a huge funding gap in the abandoned mines ecological restoration in China. It is of great research value to explore how PPP model can better introduce social capital into the low-profit ecological restoration of abandoned mines. Based on the innovation perspective of the central government's reward and punishment system, this paper constructs an evolutionary game model of "local government-social capital", analyzes the interaction and behavior mechanism of core stakeholders in the operation process of abandoned mines ecological restoration PPP mode, and discusses the influence of evolutionary equilibrium strategy and parameters change on evolutionary strategy under different scenarios by Matlab simulation. The research shows that the abandoned mines ecological restoration needs the support of the central government. When the local government lightly punishes the low-quality service of social capital, the central government needs to pay higher costs to promote all parties to actively participate in the operation and supervision of the PPP project. The revenue and cost of government supervision, the operating subsidy for social capital and the cost saved by social capital in providing bad service are the key factors affecting the evolution of the game between government and social capital. Punishment can effectively spur social capital to keep the contract and operate in the project, but the punishment effect will be ineffective without government supervision. Finally, some suggestions are put forward, such as establishing a long-term supervision mechanism and a reasonable income mechanism for PPP projects, increasing penalties for violations, attracting third parties to reduce supervision costs and strengthening communication between the two parties, so as to make the project take into account the economic performance of social capital and the social welfare of government departments, and achieve dual Pareto improvement.

A system dynamics-based model for the evolution of environmental group events

Based on the system dynamics theory, this paper establishes an environmental mass event evolution model and explores the evolution law of mass events caused by environmental problems. From a methodological point of view, the mixed-strategy evolutionary game principle and dynamic punishment measures are combined, and simulation analysis is carried out by Anylogic software, and the results show that there is no stable evolutionary equilibrium solution for the two sides of the game in the traditional asymmetric mixed-strategy game model, and after adjusting the game payoff matrix and incorporating the dynamic punishment strategy, stable evolutionary equilibrium solutions appear in the evolutionary game model, and the system begins to tend to be stabilized. The process and conclusions of the simulation experiment provide methodological reference and theoretical support for the analysis of the evolution of environmental mass events.

Impacts of Carbon Border Adjustment Mechanism on the Development of Chinese Steel Enterprises and Government Management Decisions: A Tripartite Evolutionary Game Analysis

Upon the implementation of the European Union Carbon Border Adjustment Mechanism (CBAM), substantial challenges are anticipated to impact the international trade of Chinese steel products. To safeguard the competitiveness of Chinese steel products on the global stage, this paper establishes a tripartite evolutionary game model, involving large steel enterprises, small- and medium-sized steel enterprises, and the government. The model integrates collaborative emission reduction and free-riding benefits among enterprises, along with the government’s dynamic subsidies and penalties. First, we calculate the replicator dynamic equations and conduct stability analysis to obtain the evolutionary trends and system equilibrium points in different phases of the CBAM. Then, we validate the evolutionary theoretical analysis of the model through example simulation analysis. Finally, we explore the impact of different parameters on the agents through a sensitivity analysis of parameters. The findings indicate that (1) large enterprises demonstrate greater sensitivity to CBAM, making their production structures more susceptible to changes in CBAM policies; (2) small- and medium-sized enterprises are more prone to free-riding behavior influence; (3) government intervention should be kept within appropriate boundaries, as excessive intervention may lead to strategic oscillation, with passive management being chosen by the government during the strengthening phase of CBAM; (4) elevating the price in the Chinese carbon market would slow down the structural changes in the production of Chinese steel enterprises, serving as an effective measure to counteract the impacts of CBAM. This paper provides theoretical support for how steel enterprises and the government can respond to CBAM, aiding stakeholders in selecting optimal strategies during different implementation stages and mitigating the impacts of the CBAM to the maximum extent possible.

The choice of suppliers and consumers: the evolutionary game equilibrium of platforms

ABSTRACT Platforms competition affects both the structure of the whole industry and the fate of the individual companies within it. The extant studies either simply divide the participants of a platforms war into suppliers and consumers or adopt unbounded rationality assumptions. This paper constructs a game model that includes platforms, suppliers, and the final consumers. We analyze the condition and stability of each equilibrium and the impacts of the characteristics of the core and complementary products on the equilibrium by using the method of evolutionary game. Our results show the following: (1) If the two platforms initially have separate advantages in terms of the number of suppliers or consumers, there will be an equilibrium of the coexistence; otherwise, there will be an equilibrium of single platform dominating. (2) The equilibrium of a single platform dominating is more stable than that of the coexistence of multiple platforms. (3) Incidental shocks to the number of suppliers are more likely to break the coexistence equilibrium than consumers. (4) Platforms with poor core product quality and a high price for core and complementary products can coexist with other superior platforms only if the former has more consumers and suppliers at the beginning of the competition.

Multi-group symbiotic evolutionary mechanisms of a digital innovation ecosystem: Numerical simulation and case study.

In the digital innovation ecosystem, the symbiosis mode formed between ecosystem members not only relates to their survival and development but also affects the ecosystem's symbiosis evolution mechanism. Based on symbiosis theory, this study first explores the evolutionary equilibrium strategy and its stability for three types of populations-core enterprises, digital platforms, and university research institutes-and then uses numerical simulation and a case study to explore the symbiotic evolution mechanism of the digital innovation ecosystem. The results show that: First, the digital innovation ecosystem is a complex adaptive system in which the three types of populations form different symbiotic relationships under different symbiotic modes and conduct symbiotic activities, such as value co-creation, to characterize the unique symbiotic evolutionary structure. Second, in this ecosystem, the symbiotic relationship formed by the combined values of different symbiotic coefficients between populations determines the outcome of symbiotic evolution. Third, the ideal direction of the evolution of the digital innovation ecosystem is a mutually beneficial symbiotic relationship. Thus, the symbiotic relationship between populations should be transformed into a mutually beneficial symbiotic relationships as much as possible. This study makes theoretical contributions by shedding light on the symbiotic evolution mechanism of the digital innovation ecosystem. It also offers countermeasures for the digital innovation cooperation of various stakeholders in China's digital innovation ecosystem.

Rational preference knowledge influence on the evolutionary equilibrium of carbon reduction negotiation: An exploration based on timed petri net

In the digital economy age, carbon emission reduction is perhaps the most crucial contribution affecting national activities and international negotiations. In a potential carbon reduction conflict, a rational participant expects to select a suitable strategic opinion to reach another state with improved benefit. Participants’ preferences reflect their priority ranking on multiple possible conflict solutions, directly determining the evolutionary direction and equilibrium solutions. Referring to the potential carbon reduction conflicts, Timed Petri Net for Conflict Analysis (TPNCA) is proposed as a graphical tool to explore participants’ rational preferences, state transformation, and conflict evolutionary equilibrium. The generation rule of TPNCA is designed according to carbon reduction co-operators’ rational preference knowledge. From the long-term perspective, dynamic unilateral improvement is proposed to reflect decision-makers’ strategic initiative willingness to reach end nodes. Dynamic equilibrium conditions are conducted to determine the final stability state for a conflict. This study reveals how participants’ preference knowledge and time constraints influence conflict evolutionary and dynamic equilibria. Climate group should positively engage in carbon reduction negotiations and flexibly adjust national tasks, according to real-time carbon reduction contributions. This study (1) reveals the influence of preference knowledge on conflict evolution, (2) explores the role of time constraints in determining a terminated node, (3) proposes dynamic equilibrium from the long-term perspective, and (4) helps guide participants’ strategic decision-making for mutually solving carbon reduction.

Evolution of delayed dispersal with group size effect and population dynamics

Individuals delay natal dispersal for many reasons. There may be no place to disperse to; immediate dispersal or reproduction may be too costly; immediate dispersal may mean that the individual and their relatives miss the benefits of group living. Understanding the factors that lead to the evolution of delayed dispersal is important because delayed dispersal sets the stage for complex social groups and social behavior. Here, we study the evolution of delayed dispersal when the quality of the local environment is improved by greater numbers of individuals (e.g., safety in numbers). We assume that individuals who delay natal dispersal also expect to delay personal reproduction. In addition, we assume that improved environmental quality benefits manifest as changes to fecundity and survival. We are interested in how do the changes in these life-history features affect delayed dispersal. We use a model that ties evolution to population dynamics. We also aim to understand the relationship between levels of delayed dispersal and the probability of establishing as an independent breeder (a population-level feature) in response to changes in life-history details. Our model emphasizes kin selection and considers a sexual organism, which allows us to study parent–offspring conflict over delayed dispersal. At evolutionary equilibrium, fecundity and survival benefits of group size or quality promote higher levels of delayed dispersal over a larger set of life histories with one exception. The exception is for benefits of increased group size or quality reaped by the individuals who delay dispersal. There, the increased benefit does not change the life histories supporting delay dispersal. Next, in contrast to previous predictions, we find that a low probability of establishing in a new location is not always associated with a higher incidence of delayed dispersal. Finally, we find that increased personal benefits of delayed dispersal exacerbate the conflict between parents and their offspring. We discuss our findings in relation to previous theoretical and empirical work, especially work related to cooperative breeding.

Impact of a unilateral horizontal gene transfer on the evolutionary equilibria of a population

How does the interplay between selection, mutation and horizontal gene transfer modify the phenotypic distribution of a bacterial or cell population? While horizontal gene transfer, which corresponds to the exchange of genetic material between individuals, has a major role in the adaptation of many organisms, its impact on the phenotypic density of populations is not yet fully understood. We study an elliptic integro-differential equation describing the evolutionary equilibrium of the phenotypic density of an asexual population. In a regime of small mutational variance, we characterize the solution which results from the balance between competition for a resource, mutation and horizontal gene transfer. We show that in a certain range of parameters polymorphic equilibria exist, which means that the phenotypic density may concentrate around several dominant traits. Such polymorphic equilibria result from an antagonist interplay between horizontal gene transfer and selection, while similar models which neglect the transfer lead only to monomorphic equilibria.

A three-player game model for promoting enterprise green technology innovation from the perspective of media coverage.

The objective of this study was to explore the game relationship among enterprise, the government, and the public under the new media environment, so as to provide decision-making reference for improving enterprise green technology innovation and promoting economy high-quality development with new media participation. This study constructs a three-subject evolutionary game model of enterprise, government, and public based on multi-agent relationship analysis and evolutionary game theory. In addition, the derivation of an evolutionary equilibrium strategy and numerical simulation analysis is carried out to comprehensively explore the evolution trajectory of green technology innovation system under the new media environment. (1) The system may have four stable evolutionary strategies: (1,0,0), (0,0,1), (1,0,1), and (1,1,1). (2) The initial strategy probability of various actors would affect the system evolution speed but not the evolution result, and the authenticity of new media reports is an important factor determining the system evolution of green technology innovation. (3) Numerical simulation results show that a fair and just new media environment can effectively constrain the traditional production behavior of enterprise, actively guide the public to participate in supervision, and play an alternative role to government regulation to a certain extent. This study explores the evolutionary balance strategy of green technology innovation system under the new media environment, which not only enriches relevant theories of media environment governance but also has important reference value for promoting enterprises' green technology innovation and establishing an environmental governance system jointly governed by government, enterprise, public, and media.

Separation of evolutionary timescales in coevolving species

Many coevolutionary processes, including host-parasite and host-symbiont interactions, involve one species or trait which evolves much faster than the other. Whether or not a coevolutionary trajectory converges depends on the relative rates of evolutionary change in the two species, and so current adaptive dynamics approaches generally either determine convergence stability by considering arbitrary (often comparable) rates of evolutionary change or else rely on necessary or sufficient conditions for convergence stability. We propose a method for determining convergence stability in the case where one species is expected to evolve much faster than the other. This requires a second separation of timescales, which assumes that the faster evolving species will reach its evolutionary equilibrium (if one exists) before a new mutation arises in the more slowly evolving species. This method, which is likely to be a reasonable approximation for many coevolving species, both provides straightforward conditions for convergence stability and is less computationally expensive than traditional analysis of coevolution models, as it reduces the trait space from a two-dimensional plane to a one-dimensional manifold. In this paper, we present the theory underlying this new separation of timescales and provide examples of how it could be used to determine coevolutionary outcomes from models.

Evolutionary game analysis of online game studios and online game companies participating in the virtual economy of online games.

In the context of the new economic development in the post-pandemic era, "play" labor as an important component of digital work has become an inexhaustible driving force for the growth of the digital economy. Previous research has shown that "play" labor, as an emerging business model, can effectively promote the growth of the digital economy. However, there is a relative lack of research on the dynamic evolutionary game between "play" labor suppliers represented by game studios and online gaming companies. In this study, we applied the theoretical approach of dynamic evolutionary game theory to establish a game model depicting the evolution of both parties involved in the virtual economy of online gaming. The aim was to investigate the strategic selection mechanisms and influencing factors for game studios and online gaming companies participating in the virtual economy of online gaming. By analyzing the evolutionary game path, equilibrium points, and factors influencing the evolutionary game outcome, as well as conducting numerical simulation analysis using Matlab software, we found that the incremental gains and costs resulting from the strategic choices of online gaming companies and game studios in engaging in the virtual economy of online gaming affect the evolutionary outcomes. In addition, for the probability ratio of online game studios and online game companies choosing to participate in the virtual economy of online games, whether it is online game studios or online game companies, the larger the initialization ratio, the more likely the evolution result is to develop in a mutually beneficial direction. After an in-depth analysis and discussion of the evolutionary game results, relevant policy recommendations were proposed. We hope to provide a reference for promoting online game companies to strengthen the adequate supervision of online game studios' participation in the virtual economy of online games and optimize and improve the virtual economic environment.

Firms’ corporate social irresponsibility behaviors during interplay with consumers in evolutionary game models

We employ an evolutionary game model to investigate the interaction between firms’ engagement in corporate social irresponsibility (CSI) behaviors (without violating laws) and consumers’ perception of corporate social responsibility (CSR) within a consumer market. The core paradox revolves around the trade-off between firms benefiting from pursuing economic performance without adhering to social responsibility and the maximization of social welfare achieved when firms are socially responsible, and consumers possess strong CSR perception. Through an asymmetric two-population evolutionary game model, we identify two distinct scenarios of evolutionary stable strategies based on different industrial environments. Additionally, the evolution of a healthy market is contingent upon an increase in consumers’ bargaining power, although it is also influenced by the initial states of the two-group system, resulting in path dependence as a significant feature of the system’s evolutionary equilibrium. Furthermore, we observe that the added willingness to pay for CSR, while not impacting the evolutionary outcomes, could increase the likelihood of a healthy market when consumers’ bargaining power is high. These findings underscore the diverse dynamics of firms’ CSI behaviors, which depend on transaction costs, industrial structure, and consumers’ willingness to pay, offering valuable insights from a micro perspective.

Technological Innovation Investment Channels of Industry–University–Research Alliance Enterprises and Non-Alliance Enterprises Based on Evolutionary Game

According to their resource ownership and resource acquisition channels, this paper constructs an evolutionary game model of enterprises’ technological innovation investment channels considering managers’ expectations. This results in the strategy of non-alliance firms along the first channel having a significant impact on the evolutionary equilibrium. For non-alliance enterprises, the difference in the amount of investment in the R&D stage has the same impact on the probability of such enterprises following the first channel. The number of active managers, group capacity, the difference in managers’ expectations, and the difference in the amount of technological innovation investment in the R&D stage have significant differences in the possibility of choosing the first channel between the two types of enterprises. The research conclusions can provide valuable references for enterprises to make technological innovation decisions.

Exploring the synergistic development strategy of vocational education and regional economy based on the separating equilibrium game model

Abstract To promote the synergistic development of vocational education and regional economy, this paper proposes to use the separated equilibrium game model to study vocational education and regional economy. Starting from the theoretical foundation of the components of game theory, the separated equilibrium game model oriented to the synergistic development of vocational education and regional economy is constructed by combining the game tree and the separated equilibrium game. According to the calculation formula for evolutionary stabilization strategies and equilibrium analysis, the case analysis of vocational education and regional economies is conducted. The results show that when W2 is taken as 2, 3, or 4, the system evolves towards antagonistic cooperation, but evolution is becoming increasingly slow. When W2=6, the two sides of the school and enterprise choose the strategy tends to (positive cooperation, positive cooperation), which indicates that in the school-enterprise cooperation, the government departments through tax concessions, capital subsidies and other incentives to improve the enthusiasm of enterprises is an effective method. This study analyzes the dispute of interests of school-enterprise cooperation in vocational education development from the game perspective. It provides the basis for the construction of regional economic synergistic development strategy.

Impact of emotions on the behavioral strategies of PPP project stakeholders: an RDEU evolutionary game analysis

PurposeEmotions, understood as evolving mental states, are pivotal in shaping individuals“' decision-making, especially in ambiguous information evaluation, probability estimation of events, and causality analysis. Public–private partnership (PPP) projects represent a confluence of “economic–environmental–social” dimensions, wherein stakeholder behavior follows the sequential progression of “cognition–emotion–action.” Consequently, comprehending the effects of emotional shifts on stakeholder's decision-making processes is vital to fostering the sustainability of PPP projects.Design/methodology/approachThe paper utilizes rank-dependent expected utility and evolutionary game theory to systematically examine the influence of emotional factors on stakeholders' behavior and decision-making processes within PPP projects. The paper integrates three emotional state functions—optimism, pessimism and rationality—into the PPP framework, highlighting the intricate interactions among the government, private sector, surrounding public and the media. Furthermore, the paper amalgamates the evolutionary pathways of environmental rights incidents with the media's role. Through equilibrium analysis and numerical simulation, the paper delves into the diverse interplay of emotions across different phases of the environmental rights incident, assessing the impact of these emotions on the evolutionary game's equilibrium results.FindingsEmotions significantly influence the microlevel decisions of PPP stakeholders, adapting continually based on event dynamics and media influences. When the private sector demonstrates optimism and the surrounding public leans toward rationality or pessimism, the likelihood of the private sector engaging in speculative behavior escalates, while the surrounding public refrains from adopting a supervisory strategy. Conversely, when the private sector is pessimistic and the public is optimistic, the system fails to evolve a stable strategy. However, when government regulation intensifies, the private sector opts for a nonspeculative strategy, and the surrounding public adopts a supervisory strategy. Under these conditions, the system attains a relatively optimal state of equilibrium.Originality/valueThe paper develops a game model to examine the evolutionary dynamics between the surrounding public and private sectors concerning environmental rights protection in waste incineration PPP projects. It illuminates the nature of the conflicting interests among project participants, delves into the impact of emotional factors on their decision-making processes and offers crucial perspectives for the governance of such partnerships. Furthermore, this paper provides substantive recommendations for emotional oversight to enhance governance efficacy.

Collaborative government-public efforts in driving green technology innovation for environmental governance in PPP projects: a study based on prospect theory

PurposeThe paper aims to elucidate effective strategies for promoting the adoption of green technology innovation within the private sector, thereby enhancing the value of public–private partnership (PPP) projects during the operational phase.Design/methodology/approachUtilizing prospect theory, the paper considers the government and the public as external driving forces. It establishes a tripartite evolutionary game model composed of government regulators, the private sector and the public. The paper uses numerical simulations to explore the evolutionary stable equilibrium strategies and the determinants influencing each stakeholder.FindingsThe paper demonstrates that government intervention and public participation substantially promote green technology innovation within the private sector. Major influencing factors encompass the intensity of pollution taxation, governmental information disclosure and public attention. However, an optimal threshold exists for environmental publicity and innovation subsidies, as excessive levels might inhibit technological innovation. Furthermore, within government intervention strategies, compensating the public for their participation costs is essential to circumvent the public's “free-rider” tendencies and encourage active public collaboration in PPP project innovation.Originality/valueBy constructing a tripartite evolutionary game model, the paper comprehensively examines the roles of government intervention and public participation in promoting green technology innovation within the private sector, offering fresh perspectives and strategies for the operational phase of PPP projects.