Stochastic Evolutionary Model Research Articles

Evolutionary Game Analysis of New Energy Transition Among Government, Traditional Automobile Enterprises, and Research Institutions Under the Dual Carbon Goals

This paper delves into the evolutionary dynamics of dynamic games among governments, traditional automotive enterprises, and scientific research institutions during the new energy transition process by establishing a stochastic evolutionary game model. The research focuses on exploring the conditions for the formation of system stability and the key factors influencing strategic choices. MATLAB R2021a software is employed to simulate the game process, visually demonstrating the dynamic changes in the behaviors of each participant. The results indicate that research and development (R&D) costs are a crucial consideration for scientific research institutions when deciding whether to collaborate with traditional automotive enterprises. Traditional automotive enterprises exhibit significantly higher sensitivity to government incentives for cooperation than to potential penalties for non-cooperation. Furthermore, an increase in government support costs notably dampens its enthusiasm for promoting the development of the new energy transition. Reducing government support costs and R&D costs for scientific research institutions, as well as enhancing rewards for cooperative behavior and penalties for non-cooperative behavior, can effectively facilitate the formation of evolutionarily stable strategies among governments, traditional automotive enterprises, and scientific research institutions.

Evolutionary mechanisms that promote cooperation may not promote social welfare.

Understanding the emergence of prosocial behaviours among self-interested individuals is an important problem in many scientific disciplines. Various mechanisms have been proposed to explain the evolution of such behaviours, primarily seeking the conditions under which a given mechanism can induce highest levels of cooperation. As these mechanisms usually involve costs that alter individual pay-offs, it is, however, possible that aiming for highest levels of cooperation might be detrimental for social welfare-the latter broadly defined as the total population pay-off, taking into account all costs involved for inducing increased prosocial behaviours. Herein, by comparing stochastic evolutionary models of two well-established mechanisms of prosocial behaviour-namely, peer and institutional incentives-we demonstrate that the objectives of maximizing cooperation and of maximizing social welfare are often misaligned. First, while peer punishment is often more effective than peer reward in promoting cooperation-especially with a higher impact-to-cost ratio-the opposite is true for social welfare. In fact, welfare typically decreases (increases) with this ratio for punishment (reward). Second, for institutional incentives, while maintaining similar levels of cooperation, rewards result in positive social welfare across a much broader range of parameters. Furthermore, both types of incentives often achieve optimal social welfare when their impact is moderate rather than maximal, indicating that careful planning is essential for costly institutional mechanisms to optimize social outcomes. These findings are consistent across varying mutation rates, selection intensities and game configurations. Overall, we argue for the need of adopting social welfare as the main optimization objective when designing and implementing evolutionary mechanisms for social and collective goods.

Dynamic Research on the Collaborative Governance in Urban and Rural Black-Odorous Water: A Tripartite Stochastic Evolutionary Game Perspective

The issue of black-odorous water (BOW) represents a formidable challenge to the current aquatic ecosystems, and its governance exhibits characteristics of low efficiency, susceptibility to relapse, and fragmented management under the Central Environmental Protection Inspection, thereby emerging as a dynamically complex issue in the ecological governance of urban and rural settings. This study introduces Gaussian white noise to simulate environmental uncertainty and design a stochastic evolutionary game model encompassing the central government, local governments, and societal forces based on evolutionary game theory and classical governance theories and concepts. Numerical simulations are conducted to explore trajectories of the strategic evolution of various subjects influenced by numerous factors. Results indicate that under the environment of random disturbances, the strategies of the game subjects show significant fluctuations, but actively cultivating the subject’s initial willingness facilitates collaboration governance in inspection. Moreover, joint construction of a “belief system” by multi-subjects, the intensity of inspection interventions, the integration of heterogeneous resources, and effective punitive measures all influence the governance of BOW, but the efficiency of resource allocation should be considered throughout the governance process. Recommendations are made finally for collaborative governance of urban and rural BOW, promoting the sustainable development of the ecological environment.

Manufacturing enterprises digital collaboration empowered by Industrial Internet Platform: A multi-agent stochastic evolutionary game

Digital transformation is a critical way to improve the resilience of the manufacturing industry chain. However, the current digitalization of manufacturing enterprises lacks upstream and downstream linkage. If the level of digitization of upstream and downstream enterprises differs significantly, it will increase transaction costs. Digital transformation with the help of industrial Internet platform has become a trend. For this reason, this study deeply explores the influence mechanism of digitalization collaboration of manufacturing enterprises under the empowerment of industrial Internet platform. This paper constructs a stochastic evolutionary game model with core manufacturing enterprise, supplier and local government as the main players. Consider stochastic differential equations to analyze the stability conditions of game subjects, and explore different incentive mechanisms on enterprise strategy. The results show that the data security of the platform and the network effect coefficients significantly affect the strategy selection results of the players. Additionally, the change of environmental noise affects the strategy evolution process of the subject, and the supplier strategy is more affected by environmental noise compared to the core manufacturing enterprises. Furthermore, the dynamic incentive effect of the government is better than the static incentive, which can better promote the digital collaboration of manufacturing enterprises. Dynamic penalties are less effective than static penalties. The study’s conclusions can provide a reference for the government to implement the gradient digitalization incentive policy and provide a theoretical basis for promoting digital collaboration in manufacturing enterprises.

How to escape the dilemma of carbon emission reduction policies implementation under Chinese fiscal decentralization?

As the world's largest energy consumer and carbon emitter, China has undertaken a series of low-carbon policies. However, its top-down authoritarian governance, coupled with economic decentralization, challenges policy effectiveness. To facilitate the implementation of incentive-compatible carbon emission reduction policies, this study proposes a tripartite stochastic evolutionary game model involving the central government, local governments, and enterprises. Replicator dynamic equations are then employed to assess how uncertainty shapes participants' behavioral choices. Furthermore, a real-case example validates the theoretical findings and supports subsequent arguments: (1) initial strategy choices by stakeholders influence their transitions but have minimal long-term impact on the final convergence pattern; (2) stakeholders' dedicated efforts, especially central government supervision, shape evolutionary outcomes during policy implementation; (3) the escalation of penalties contributes to policy execution, while transfer payment allocation warrants thorough evaluation as it affects the strategies of both local governments and enterprises; and (4) the incorporation of random elements introduces disruptions in stakeholder evolutionary paths, resulting in deviations and fluctuations from expected patterns. This study not only highlights the importance of resolving the dilemma in implementing emission reduction policies through effective coordination among stakeholders but also reduces uncertainty related to unobserved factors, ensuring a comprehensive range of game outcomes.

A branching stochastic evolutionary model of the B-cell repertoire

We propose a stochastic framework to describe the evolution of the B-cell repertoire during germinal center (GC) reactions. Our model is formulated as a multitype age-dependent branching process with time-varying immigration. The immigration process captures the mechanism by which founder B cells initiate clones by gradually seeding GC over time, while the branching process describes the temporal evolution of the composition of these clones. The model assigns a type to each cell to represent attributes of interest. Examples of attributes include the binding affinity class of the B cells, their clonal family, or the nucleotide sequence of the heavy and light chains of their receptors. The process is generally non-Markovian. We present its properties, including as t→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t\\rightarrow \\infty $$\\end{document} when the process is supercritical, the most relevant case to study expansion of GC B cells. We introduce temporal alpha and beta diversity indices for multitype branching processes. We focus on the dynamics of clonal dominance, highlighting its non-stationarity, and the accumulation of somatic hypermutations in the context of sequential immunization. We evaluate the impact of the ongoing seeding of GC by founder B cells on the dynamics of the B-cell repertoire, and quantify the effect of precursor frequency and antigen availability on the timing of GC entry. An application of the model illustrates how it may help with interpretation of BCR sequencing data.

Three modes of evolution?Remarks on rates of evolution and time scaling.

Rates of evolution get smaller when they are measured over longer time intervals. As first shown by Gingerich, rates of morphological change measured from fossil time series show a robust minus-one scaling with time span, implying that evolutionary changes are just as large when measured over a hundred years as when measured over a hundred-thousand years. On even longer time scales, however, the scaling shifts toward a minus-half exponent consistent with evolution behaving as Brownian motion, as commonly observed in phylogenetic comparative studies. Here, I discuss how such scaling patterns arise, and I derive the patterns expected from standard stochastic models of evolution. I argue that observed shifts cannot be easily explained by simple univariate models, but require shifts in mode of evolution as time scale is changing. To illustrate this idea, I present a hypothesis about three distinct, but connected, modes of evolution. I analyze the scaling patterns predicted from this, and use the results to discuss how rates of evolution should be measured and interpreted. I argue that distinct modes of evolution at different time scales act to decouple micro- and macroevolution, and criticize various attempts at extrapolating from one to the other.

Decision Analysis of Cold Chain Supply Chain Based on a Stochastic Evolution Model

Accelerating the development of cold chain logistics for agricultural products is not only an objective requirement for the development of agricultural product circulation but also a necessary demand to promote rural revitalization and upgrade agricultural consumption. Addressing the evolutionary problems of cold chain transportation in uncertain environments, this study considers the actual stochastic disturbances in the cold chain supply chain system, introducing Gaussian white noise to reflect the random perturbations experienced during the evolution of the cold chain. A three-party stochastic evolutionary game model is established involving farmers, logistics enterprises, and government regulatory authorities. Based on this model, numerical simulation analysis is conducted to explore the effects of different factors such as the intensity of random disturbances and the loss transfer coefficient on the fluctuation of strategic choices of the entities and the convergence speed to a stable state during evolution. Finally, combining the results of numerical simulation, relevant policies and recommendations are proposed to provide insights and guidance for the development of cold chain logistics in agricultural products.

A stochastic and time-delay evolutionary game of food safety regulation under central government punishment mechanism

Food safety is a pressing issue affecting public health, and strengthening food safety regulation has become a widespread consensus. This study addresses the three-party game involving food production enterprises, third-party testing agencies, and government regulatory authorities. Considering the influence of random disturbances and time delays on the strategy-choosing and behavioral evolution of game players, a three-party stochastic evolutionary game model for food safety regulation with time delays is established. The stability of the model is analyzed by using Lyapunov's method, and the strategy evolution of the game players is investigated while combining numerical simulations. The study shows that the net benefit of the players' expected strategies is key in determining whether the overall game system can reach the optimal equilibrium. The level of penalties imposed by the central government on local government regulators is key to food safety. The main factors influencing the strategy-choosing of game players are the level of penalties imposed by the local government regulators on third-party testing agencies, together with the supervision costs of the local government regulators. Random disturbances have a certain impact on strategy-choosing of the game players, with a greater impact on testing agencies, followed by food production enterprises, and a weaker impact on government regulatory authorities. The time delay factors exhibit a certain delay effect on the evolutionary path of strategy-choosing among the game players, which aligns with the actual situation. The findings of the study have implications for food safety regulation.

Stochastic evolutionary game analysis of tacit knowledge sharing in patent commercialization

AbstractGiven the rapid prevalence and advancement of patent commercialization, tacit knowledge sharing during this process is increasingly being scrutinized. To explore the factors affecting tacit knowledge sharing in patent commercialization, this paper constructed a tripartite stochastic evolutionary game model to analyze the complex game interaction between inventors, enterprises, and patent intermediaries. Due to uncertainty in the external environment, Gaussian white noise was introduced into replicator dynamic equations, and numerical simulation was used to describe the tripartite dynamic evolution. The results showed the following: (1) inventors and enterprises with similar levels of relevant capabilities are more likely to achieve better results in sharing tacit knowledge. (2) The implementation of an effective market reputation evaluation system has the potential to enhance implicit knowledge sharing in the realm of patent commercialization. (3) The percentage of payments of the two‐stage payment contract will affect the behavior of inventors and enterprises. (4) The stability of the equilibrium solution is closely tied to the intensity of Gaussian white noise, which can lead to deviations from the original trajectory of equilibrium strategies. Greater external uncertainty makes tacit knowledge sharing more challenging. This study will provide constructive suggestions for promoting tacit knowledge sharing among participants in patent commercialization.

Evolution analysis of low-carbon cooperation of service providers based on Moran process in cloud manufacturing.

Low-carbon cooperation among cloud manufacturing service providers is one way to achieve carbon peak and neutrality. Such cooperation is related to the benefits to service providers adopting low-carbon strategies and stochastic factors such as government low-carbon policies, providers' environmental awareness, and demanders' low-carbon preferences. Focusing on the evolutionary process of service providers' low-carbon strategy selection under uncertain factors, a stochastic evolutionary game model is constructed based on the Moran process, and the equilibrium conditions for low-carbon cooperation among providers are analyzed under benefit-dominated and stochastic factor-dominated situations. Through numerical simulation, the effects of the cloud platform's cost-sharing coefficient for low-carbon investment, matching growth rate, carbon trading price, and group size on providers' low-carbon strategy evolution are analyzed. The research results show that increasing the cloud platform's low-carbon cost-sharing, carbon trading price, and group size can promote low-carbon cooperation among service providers. With greater low-carbon investment costs and greater stochastic factor interference, the providers' enthusiasm for low-carbon cooperation decreases. This study fills the research gap in the low-carbon cooperation evolution of cloud manufacturing providers based on the stochastic evolutionary game and provides decision-making suggestions for governments and cloud platforms to encourage provider participation in low-carbon cooperation and for providers to adopt low-carbon strategies.

Modeling the Effect of Spatial Structure on Solid Tumor Evolution and Circulating Tumor DNA Composition.

Circulating tumor DNA (ctDNA) monitoring, while sufficiently advanced to reflect tumor evolution in real time and inform cancer diagnosis, treatment, and prognosis, mainly relies on DNA that originates from cell death via apoptosis or necrosis. In solid tumors, chemotherapy and immune infiltration can induce spatially variable rates of cell death, with the potential to bias and distort the clonal composition of ctDNA. Using a stochastic evolutionary model of boundary-driven growth, we study how elevated cell death on the edge of a tumor can simultaneously impact driver mutation accumulation and the representation of tumor clones and mutation detectability in ctDNA. We describe conditions in which invasive clones are over-represented in ctDNA, clonal diversity can appear elevated in the blood, and spatial bias in shedding can inflate subclonal variant allele frequencies (VAFs). Additionally, we find that tumors that are mostly quiescent can display similar biases but are far less detectable, and the extent of perceptible spatial bias strongly depends on sequence detection limits. Overall, we show that spatially structured shedding might cause liquid biopsies to provide highly biased profiles of tumor state. While this may enable more sensitive detection of expanding clones, it could also increase the risk of targeting a subclonal variant for treatment. Our results indicate that the effects and clinical consequences of spatially variable cell death on ctDNA composition present an important area for future work.

Understanding the Complex Adaptive Characteristics of Cross-Regional Emergency Collaboration in China: A Stochastic Evolutionary Game Approach

Regional integration and pairing assistance are two forms of cross-regional emergency collaboration practice carried out by the Chinese government. Based on the Chinese government’s emergency management practice, evolutionary game models of cross-regional emergency collaboration were constructed. Further, the traditional evolutionary game model was improved by introducing the stochastic process, and Gaussian white noise was introduced as a random disturbance. The stochastic evolutionary game model was constructed, and the existence and stability of the equilibrium solutions of the two kinds of stochastic evolutionary game systems for cross-regional emergency collaboration were verified based on the stability discrimination theorem of stochastic differential equations. We used numerical simulations to simulate the evolution trajectories of the regional integration and the pairing assistance stochastic evolutionary game system. In the regional integration game system, when the efficiency of emergency collaboration, the emergency capital stock, and the externality coefficients are higher, positive emergency strategies are more likely to become the stable state of the game subjects’ strategy selection. In the pairing assistance game system, the efficiency of emergency collaboration, the rewards and benefits from the central government, and the matching degree between governments all had positive effects on the formation of the positive emergency strategies of the game subjects. In addition, the pairing assistance mechanism for sustainable development requires external support from the central government.

Social Conflict and the Evolution of Unequal Conventions

Abstract We propose a theory of social norms (or conventions) that implement substantial levels of inequality between men and women, ethnic groups, and classes and that persist over long periods of time despite being inefficient and not supported by formal institutions. Consistent with historical cases, we extend the standard asymmetric stochastic evolutionary game model to allow subpopulation sizes to differ and idiosyncratic rejection of a status quo convention to be intentional to some degree (rather than purely random as in the standard evolutionary models). In this setting, if idiosyncratic play is sufficiently intentional and the subordinate class is sufficiently large relative to the elite, then risk-dominated conventions that are both more unequal and inefficient relative to alternative conventions will be stochastically stable and may persist for long periods. We show that the same is true in a general bipartite network of the population if most of the subordinate groups interactions are local, while the elite is more “cosmopolitan”. We apply the model to the evolution of wage conventions on the bipartite network of workers and employers, and find that an unequal monopsonistic wage convention is robust to the idiosyncratic play of workers that otherwise might displace it.

Stochastic Evolutionary Game Model of Hot Topics Propagation for Network Public Opinion

Due to the rapid propagation and significant impact, the network public opinion of hot topics has become a concern of the social public and governments. The existing models based on the evolutionary game cannot reflect the real-world propagation of hot topics under uncertain environmental interference. And few researchers analyze the early intervention timing of the government on hot topics based on stochastic evolutionary game theory. To solve these problems, the government intervention parameters of punishment intensity, intervention delay, and intervention probability are introduced to build a three-party stochastic evolutionary game model of “media-netizen-government” in the multi-agent system under the scene of hot topics propagation. Then, the stochastic differential equation is expanded and simulated by the explicit forward Euler numerical method. Finally, simulation experiments are conducted to quantitatively analyze the random evolutionary process and the government intervention timing by adjusting key parameters, which can provide the optimal timing and suggestions for governments to intervene in hot topics propagation.

How to achieve carbon abatement in aviation with hybrid mechanism? A stochastic evolutionary game model

Aviation carbon emissions are growing as the volume of aviation traffic continues to increase, both exacerbating global greenhouse gas emissions and increasing the resistance to green aviation development. To effectively promote aviation carbon abatement, this paper, based on the hybrid mechanism composed of carbon trading and taxation, a tripartite Itô stochastic evolutionary game model is first constructed. The complex game interactions among the administration, major airlines, and minor airlines are analyzed. Second, we use Gaussian white noise as the ambient uncertainty and apply stochastic Taylor expansion to find the numerical approximation solution. Finally, through numerical simulations, the decision-making behavior of stakeholders and their sensitivity to key influencing factors are illustrated. The study shows that different variables have differential effects on stakeholders’ strategic choices in terms of convergence speed, change speed, and stability. Starting from three different regulatory paths, this study provides insights into the priority and direction of adjusting relevant variables, thereby offering guidance for policymakers and managers in effectively regulating aviation carbon abatement.

A tripartite stochastic evolutionary game model of complex technological products in a transnational supply chain

The effective operation of a transnational supply chain under economic globalization is a key way to promote scientific and technological progress and a realistic requirement for the development of social productivity. However, the long-term dynamic interaction between the transnational operation decision-making behavior and the random interferences owing to multiple uncertain factors is difficult to explain using traditional game theory. Therefore, we establish a tripartite stochastic evolutionary game model among multinational corporations, foreign distributors, and the government. We consider It̂o’s stochastic differential equation to analyze stability conditions through stability analysis, numerical simulation, and in-depth case simulation. The results show that the game’s evolutionarily stable strategy comprises eight pure strategies, and obtains the critical value of the key parameters which can effectively guide the evolution of the multinational supply chain to a reasonable long-term optimal path. We innovatively use the tripartite evolutionary path iterative algorithm to propose a dynamic strategy selection scheme and find that the consumer preference for complex technology products significantly affects the tripartite strategy.

Stochastic evolutionary game analysis of food cooperation among countries along the Belt and Road from the perspective of food security

IntroductionIn recent years, the combination of the public health crisis and the climate crisis has greatly weakened the resilience of food systems. The Belt and Road food cooperation will make outstanding contributions to consolidate food security and reduce global poverty in countries along the Belt and Road.MethodsThis paper constructs a three-party stochastic evolutionary game model from the perspective of food security, distinguishes the difference between large and small countries by calculating the cereal self-sufficiency rate, which studies the cooperation strategy with the Belt and Road cereal large countries, cereal small countries and regulatory committees as the object. In addition, we introduce the Gaussian white noise characteristics to characterize the stochastic disturbance of the game system. Then we combine the mathematical derivation of the stochastic evolutionary game analysis with the simulation method, examine the effect of the stochastic disturbance factors on the cooperation, and find out the factors that affect the cooperation. And finally verifies the model and proves the reasonableness and practicability of the model.ResultsThe stochastic evolutionary game model analyzes the interaction of stochastic disturbance and influencing factors from a dynamic perspective, and the stability of evolution is related to the strength of Gaussian white noise. The level of effort of large cereal countries and the incentives of regulatory committees can have a positive impact, but high income in small cereal countries can lead to instability in the strategic choices of other players.DiscussionTaking the countries along the Belt and Road as the research object, Gaussian white noise is introduced to describe the stochastic external environment, discriminate the stability of the game system through stochastic differential equations, and analyze the influencing factors of the dynamic behavioral strategies of the parties in combination with simulation methods. To improve the capacity of national food security governance and help improve the resilience of the world food system.

A stochastic evolutionary dynamic game model for analyzing the ride-sourcing market with limited platform reputation

Ride-sourcing services have become increasingly vital in meeting on-demand mobility needs. However, safety issues and public health concerns are obstacles for passengers' trust in ride-sourcing service providers. In this paper, we propose a stochastic evolutionary dynamic game approach to modeling and managing the ride-sourcing market with limited platform reputation, and interpret some intriguing phenomena in terms of passengers' and drivers' travel behavior, e.g. survivor bias, reciprocity, and tragedy of the commons. A stochastic state dynamic game model is formulated to capture complicated interactions among three games/states, i.e. trust game, complaint game, and rating-based game. The stationary distribution of each state and transitional probabilities are deducted from the stochastic game theory. We analyze the ride-sourcing system's evolution and reveal its intrinsic mechanism based on the model. We found that, if the governmental support for complaints is inadequate and passengers bear the high complaint costs, drivers will be more inclined to compensate passengers privately (i.e. reciprocity) to escape punishment for unqualified service. As a result, the service quality will deteriorate in the long run. To prevent the deterioration of service quality, we explore adaptive pricing strategies for the ride-sourcing platform and suggest managerial strategies for the government. This paper bridges the gap between the dynamic evolution and the mechanism of trust in ride-sourcing services, which has been seldom studied in the literature. All of the analytical results are illustrated by numerical experiments.

Effect of update rule transition triggered by Q-learning algorithm in evolutionary prisoner's dilemma game involving extortion

Most studies have shown that the heterogeneity of update rules has an important impact on evolutionary game dynamics. In the meanwhile, Q-learning algorithm has gained attention and extensive study in evolutionary games. Therefore, a mixed stochastic evolutionary game dynamic model involving extortion strategy is constructed by combining imitation and aspiration-driven updating rules. During the evolution of the model, individuals will use the Q-learning algorithm which is a typical self-reinforcement learning algorithm to determine which update rule to adopt. Herein, through numerical simulation analyses, it is found that the mixed stochastic evolutionary game dynamic model affected by the Q-learning algorithm ensures the survival of cooperators in the grid network. Moreover, the cooperators cannot form a cooperation cluster in the grid network but will form a chessboard-like distribution with extortioners to protect cooperators from the invasion of defectors. In addition, a series of results show that, before the evolution turns into steady state, our model increases the number of nodes utilizing the average aspiration-driven update rule, thereby promoting the emergence of chessboard-like distribution. Overall, our study may provide some interesting insights into the development of cooperative behavior in the real world.