Analyzing the use of non-pharmaceutical personal protective measures through self-interest and social optimum for the control of an emerging disease.

Non-pharmaceutical personal protective (NPP) measures such as face masks use, and hand and respiratory hygiene can be effective measures for mitigating the spread of aerosol/airborne diseases, such as COVID-19, in the absence of vaccination or treatment. However, the usage of such measures is constrained by their inherent perceived cost and effectiveness for reducing transmission risk. To understand the complex interaction of disease dynamics and individuals decision whether to adopt NPP or not, we incorporate evolutionary game theory into an epidemic model such as COVID-19. To compare how self-interested NPP use differs from social optimum, we also investigated optional control from a central planner's perspective. We use Pontryagin's maximum principle to identify the population-level NPP uptake that minimizes disease incidence by incurring the minimum costs. The evolutionary behavior model shows that NPP uptake increases at lower perceived costs of NPP, higher transmission risk, shorter duration of NPP use, higher effectiveness of NPP, and shorter duration of disease-induced immunity. Though social optimum NPP usage is generally more effective in reducing disease incidence than self-interested usage, our analysis identifies conditions under which both strategies get closer. Our model provides new insights for public health in mitigating a disease outbreak through NPP.

Evolutionary game analysis between regional governments and shipping companies: Considering the impact of government subsidy on shipping companies.

Maritime agencies are imposing stricter limits on fuel sulfur content, and regional governments are encouraging the reduction of various emissions through subsidies. In this study, an evolutionary game model is constructed to analyze the interaction between regional governments and shipping companies under the fixed and dynamic subsidies. The sensitivity analysis reveals the effect of parameters on stabilization strategies. The results show that the bilateral stakeholders can adopt stabilization strategies under dynamic subsidies. The fines, maximum subsidies and extra cost paid by regional governments have a significant impact on these strategies. To reduce the dependence of shipping companies on subsidy policies, it is recommended to improve the LSFO refining technology in the future. Expanding the implementation scope of LSFO subsidy policies will increase the utilization of LSFO by shipping companies. This study offers insights for governments to optimize the LSFO subsidy policy and shipping companies to choose sulfur oxides reduction approaches.

The evolution of social behaviors and risk preferences in settings with uncertainty.

Humans update their social behavior in response to past experiences and changing environments. Behavioral decisions are further complicated by uncertainty in the outcome of social interactions. Faced with uncertainty, some individuals exhibit risk aversion while others seek risk. Attitudes toward risk may depend on socioeconomic status; and individuals may update their risk preferences over time, which will feedback on their social behavior. Here, we study how uncertainty and risk preferences shape the evolution of social behaviors. We extend the game-theoretic framework for behavioral evolution to incorporate uncertainty about payoffs and variation in how individuals respond to this uncertainty. We find that different attitudes toward risk can substantially alter behavior and long-term outcomes, as individuals seek to optimize their rewards from social interactions. In a standard setting without risk, for example, defection always overtakes a well-mixed population engaged in the classic Prisoner's Dilemma, whereas risk aversion can reverse the direction of evolution, promoting cooperation over defection. When individuals update their risk preferences along with their strategic behaviors, a population can oscillate between periods dominated by risk-averse cooperators and periods of risk-seeking defectors. Our analysis provides a systematic account of how risk preferences modulate, and even coevolve with, behavior in an uncertain social world.

Analysis of production decision-making evolution of steel enterprises under carbon border adjustment mechanism.

This work explored the changes in production decision-making trends of Chinese steel enterprises under the influence of the carbon border adjustment mechanism. First, using evolutionary game theory, the interactive mechanism of complex production strategies among steel enterprises considering the carbon border adjustment mechanism was studied, including the impact of government subsidy coefficients, additional profits and carbon tax prices on enterprise decision-making. Second, the influence of key parameters on the dynamic evolutionary process was analysed. On this basis, the empirical simulation method was used to verify the game model and the main conclusions. Finally, the sensitivity analysis of the selected parameters was determined using Matlab software. The results showed that additional profits from green investment, government subsidy coefficients, input-output values and carbon tax prices had a higher impact on the evolution of enterprise production strategies. The results of this study provide a decision-making basis for the selection of future production methods for steel enterprises.

Theoretical analyses for the evolution of biogenic volatile organic compounds (BVOC) emission strategy.

Plants emit biogenic volatile organic compounds (BVOCs) as signaling molecules, playing a crucial role in inducing resistance against herbivores. Neighboring plants that eavesdrop on BVOC signals can also increase defenses against herbivores or alter growth patterns to respond to potential risks of herbivore damage. Despite the significance of BVOC emissions, the evolutionary rationales behind their release and the factors contributing to the diversity in such emissions remain poorly understood. To unravel the conditions for the evolution of BVOC emission, we developed a spatially explicit model that formalizes the evolutionary dynamics of BVOC emission and non-emission strategies. Our model considered two effects of BVOC signaling that impact the fitness of plants: intra-individual communication, which mitigates herbivore damage through the plant's own BVOC signaling incurring emission costs, and inter-individual communication, which alters the influence of herbivory based on BVOC signals from other individuals without incurring emission costs. Employing two mathematical models-the lattice model and the random distribution model-we investigated how intra-individual communication, inter-individual communication, and spatial structure influenced the evolution of BVOC emission strategies. Our analysis revealed that the increase in intra-individual communication promotes the evolution of the BVOC emission strategy. In contrast, the increase in inter-individual communication effect favors cheaters who benefit from the BVOCs released from neighboring plants without bearing the costs associated with BVOC emission. Our analysis also demonstrated that the narrower the spatial scale of BVOC signaling, the higher the likelihood of BVOC evolution. This research sheds light on the intricate dynamics governing the evolution of BVOC emissions and their implications for plant-plant communication.

Impact of discrepant accumulations strategy on collective cooperation in multilayer networks.

Understanding large-scale cooperation among related individuals has been one of the largest challenges. Since humans are in multiple social networks, the theoretical framework of multilayer networks is perfectly suited for studying this fascinating aspect of our biology. To that effect, we here study the cooperation in evolutionary game on interdependent networks. Importantly, a part of players are set to adopt Discrepant Accumulations Strategy. Players employing this mechanism not only use their payoffs in the multilayer network as the basis for the updating process as in previous experiments, but also take into account the similarities and differences in strategies across different layers. Monte Carlo simulations demonstrate that considering the similarities and differences in strategies across layers when calculating fitness can significantly enhance the cooperation level in the system. By examining the behavior of different pairing modes within cooperators and defectors, the equilibrium state can be attributed to the evolution of correlated pairing modes between interdependent networks. Our results provide a theoretical analysis of the group cooperation induced by the Discrepant Accumulations Strategy. And we also discuss potential implications of these findings for future human experiments concerning the cooperation on multilayer networks.

Enhancing vaccination strategies for epidemic control through effective lockdown measures.

Evolutionary epidemiology models have substantially impacted the study of various infections and prevention methods in the biology field. These models are called Susceptible, Lockdown, Vaccinated, Infected, and Recovered (SLVIR) epidemic dynamics. We explore how human behavior, particularly in the context of disease transmission, is influenced by two intervention strategies: vaccination and lockdown, both of which are grounded in the principles of evolutionary game theory (EGT). This comprehensive study using evolutionary game theory delves into the dynamics of epidemics, explicitly focusing on the transition rate from susceptibility to immunity and susceptibility to lockdown measures. Our research involves a thorough analysis of the structural aspects of the SLVIR epidemic model, which delineates disease-free equilibria to ensure stability in the system. Our investigation supports the notion that implementing lockdown measures effectively reduces the required level of vaccinations to curtail the prevalence of new infections. Furthermore, it highlights that combining both strategies is particularly potent when an epidemic spreads rapidly. In regions where the disease spreads comparatively more, our research demonstrates that lockdown measures are more effective in reducing the spread of the disease than relying solely on vaccines. Through significant numerical simulations, our research illustrates that integrating lockdown measures and efficient vaccination strategies can indirectly lower the risk of infection within the population, provided they are both dependable and affordable. The outcomes reveal a nuanced and beneficial scenario where we examine the interplay between the evolution of vaccination strategies and lockdown measures, assessing their coexistence through indicators of average social payoff.

Research on distribution strategy of logistics enterprise alliance based on three-party evolution game.

Currently, collaborative distribution models have not reached the optimal state of carbon emissions. The cost of additional low-carbon expenditures and the problem of carbon data verification have led to the lack of motivation for reducing emissions among collaborative distribution enterprises. Therefore, how to incentivize them to adopt the low-carbon model is crucial for achieving low-carbon goal. By relying on a government-led digital platform, this paper designs a dual low-carbon incentive strategy to encourage enterprise-alliance to adopt a low-carbon distribution model. In this paper, we first construct an evolutionary game model of the government, enterprise-alliance and end-users; then we explore the conditions of the three-party equilibrium evolution strategy by solving the model and analyzing the stability; and finally, we conduct simulation validation and results analysis with the help of MATLAB. In summary, we found that government punishment is more effective at regulating enterprise-alliance than reward. End-users' behavior is affected by the costs they need to bear, and they no longer support enterprise-alliance to carry out collaborative low-carbon distribution above a certain threshold.

Interaction intensity in strategic fitness: A quantifying yardstick of selection optimization for evolutionary game.

The notion of the fitness of a strategy has been assimilated as the reproductive success in the evolutionary game. Initially, this fitness was tied to the game's pay-off and the strategy's relative frequency. However, density dependence becomes exigent in order to make ecologically reliable fitness. However, the contributions of each different type of interaction to the species's overall growth process were surprisingly under-explored. This oversight has occasionally led to either more or less prediction of strategy selection compared to the actual possibility. Moreover, density regulation of the population has always been analysed in a general way compared to strategy selection. In this context, our study introduces the concept of mean relative death payoff, which helps in assessing interaction intensity coefficients and integrates them into strategic fitness. Based on this fitness function, we develop the frequency-density replicator dynamics, which eventually provides distinguishing criteria for directional and balancing selection. Our optimized, evolutionarily stable strategy emerges as a superior alternative to the conventional trade-off between selection forces and ecological processes. More significantly, mean relative death pay-off has both conditional and quantitative roles in getting a stable population size. As a case study, we have extensively analysed the evolution of aggression using the Hawk-Dove game. We have shown that pure Dove selection is always beneficial for species growth rather than pure Hawk selection, and the condition of selection is dependent on external mortality pressure. However, the condition of coexistence is independent of external mortality pressure, representing a strong evolutionary selection that optimizes population density governed by interaction intensity.

A study of the evolutionary game of carbon offset involving tourism stakeholders under incentive and constraint mechanisms.

Tourism carbon offsetting is a crucial pathway to achieving peak carbon and carbon neutrality in the tourism industry. Accurately grasping the collaborative evolutionary mechanisms among local governments, tourism enterprises, and tourists is key to promoting the implementation of tourism carbon offsetting. By constructing an evolutionary game model involving local governments, tourism enterprises, and tourists in carbon offsetting, this study uses MATLAB to simulate the evolutionary stable strategies under various conditions. Additionally, it dynamically simulates the collaborative strategies of the three parties under the influence of local government incentive and constraint mechanisms. The results indicate that under strong governmental constraint mechanisms, there is a promotion of active participation in carbon offsetting by local governments, tourism enterprises, and tourists. Incentive policies at certain levels also play a positive guiding role. As incentives increase, local subsidies and intervention costs also rise, leading to an evolution towards less enthusiastic participation among the three parties. Appropriately balanced government incentives and penalties are beneficial in achieving an equilibrium of benefits among multiple stakeholders involved in carbon offsetting, thus helping to attain carbon neutrality goals.

The paradigm of tax-reward and tax-punishment strategies in the advancement of public resource management dynamics.

In contemporary society, the effective utilization of public resources remains a subject of significant concern. A common issue arises from defectors seeking to obtain an excessive share of these resources for personal gain, potentially leading to resource depletion. To mitigate this tragedy and ensure sustainable development of resources, implementing mechanisms to either reward those who adhere to distribution rules or penalize those who do not, appears advantageous. We introduce two models: a tax-reward model and a tax-punishment model, to address this issue. Our analysis reveals that in the tax-reward model, the evolutionary trajectory of the system is influenced not only by the tax revenue collected but also by the natural growth rate of the resources. Conversely, the tax-punishment model exhibits distinct characteristics when compared with the tax-reward model, notably the potential for bistability. In such scenarios, the selection of initial conditions is critical, as it can determine the system's path. Furthermore, our study identifies instances where the system lacks stable points, exemplified by a limit cycle phenomenon, underscoring the complexity and dynamism inherent in managing public resources using these models.

An innovative fractional-order evolutionary game theoretical study of personal protection, quarantine, and isolation policies for combating epidemic diseases.

This study uses imposed control techniques and vaccination game theory to study disease dynamics with transitory or diminishing immunity. Our model uses the ABC fractional-order derivative mechanism to show the effect of non-pharmaceutical interventions such as personal protection or awareness, quarantine, and isolation to simulate the essential control strategies against an infectious disease spread in an infinite and uniformly distributed population. A comprehensive evolutionary game theory study quantified the significant influence of people's vaccination choices, with government forces participating in vaccination programs to improve obligatory control measures to reduce epidemic spread. This model uses the intervention options described above as a control strategy to reduce disease prevalence in human societies. Again, our simulated results show that a combined control strategy works exquisitely when the disease spreads even faster. A sluggish dissemination rate slows an epidemic outbreak, but modest control techniques can reestablish a disease-free equilibrium. Preventive vaccination regulates the border between the three phases, while personal protection, quarantine, and isolation methods reduce disease transmission in existing places. Thus, successfully combining these three intervention measures reduces epidemic or pandemic size, as represented by line graphs and 3D surface diagrams. For the first time, we use a fractional-order derivate to display the phase-portrayed trajectory graph to show the model's dynamics if immunity wanes at a specific pace, considering various vaccination cost and effectiveness settings.

Evolutionary Game Dynamics with Environmental Feedback in a Network with Two Communities.

Recent developments of eco-evolutionary models have shown that evolving feedbacks between behavioral strategies and the environment of game interactions, leading to changes in the underlying payoff matrix, can impact the underlying population dynamics in various manners. We propose and analyze an eco-evolutionary game dynamics model on a network with two communities such that players interact with other players in the same community and those in the opposite community at different rates. In our model, we consider two-person matrix games with pairwise interactions occurring on individual edges and assume that the environmental state depends on edges rather than on nodes or being globally shared in the population. We analytically determine the equilibria and their stability under a symmetric population structure assumption, and we also numerically study the replicator dynamics of the general model. The model shows rich dynamical behavior, such as multiple transcritical bifurcations, multistability, and anti-synchronous oscillations. Our work offers insights into understanding how the presence of community structure impacts the eco-evolutionary dynamics within and between niches.

How can the recycling of power batteries for EVs be promoted in China? A multiparty cooperative game analysis.

While electric vehicles (EVs) are developing at a high speed in China, the power battery market is facing a decommissioning peak. The problem is that the recycling situation of domestic power batteries is not ideal, partly due to neglect by consumers. By considering the recycling system, mode, and policy of China's EV power batteries, we construct a tripartite evolutionary game model of the government, consumers and EV manufacturers; analyse the stable strategy adjustment mechanisms of tripartite participation in this recycling cooperation game; and simulate the tripartite evolutionary game. The results show that when the initial willingness of the government, consumers and EV manufacturers to recycle power batteries is not strong, the government takes the lead, driving EV manufacturers and consumers to participate in power battery recycling. When the government, consumers and EV manufacturers have medium or high levels of initial willingness, the government evolves and chooses a nonregulation strategy. In addition, by simulating the impact of changes in consumer-related influencing factors on this tripartite evolutionary game, we find that subsidies for recycling power batteries are a key factor affecting consumers' strategy choices and that boosting recycling compensation for consumers can improve their enthusiasm to participate in such recycling. Therefore, to improve the recycling of power batteries for EVs, in terms of both efficiency and percentage of deployment, the Chinese government should strengthen public education on power battery recycling, further integrate informal recycling channels, and balance the distribution of profits among consumers for recycling compensation.

Persistence in repeated games encourages the evolution of spite.

Social behavior is divided into four types: altruism, spite, mutualism, and selfishness. The former two are costly to the actor; therefore, from the perspective of natural selection, their existence can be regarded as mysterious. One potential setup which encourages the evolution of altruism and spite is repeated interaction. Players can behave conditionally based on their opponent's previous actions in the repeated interaction. On the one hand, the retaliatory strategy (who behaves altruistically when their opponent behaved altruistically and behaves non-altruistically when the opponent player behaved non-altruistically) is likely to evolve when players choose altruistic or selfish behavior in each round. On the other hand, the anti-retaliatory strategy (who is spiteful when the opponent was not spiteful and is not spiteful when the opponent player was spiteful) is likely to evolve when players opt for spiteful or mutualistic behavior in each round. These successful conditional behaviors can be favored by natural selection. Here, we notice that information on opponent players' actions is not always available. When there is no such information, players cannot determine their behavior according to their opponent's action. By investigating the case of altruism, a previous study (Kurokawa, 2017, Mathematical Biosciences, 286, 94-103) found that persistent altruistic strategies, which choose the same action as the own previous action, are favored by natural selection. How, then, should a spiteful conditional strategy behave when the player does not know what their opponent did? By studying the repeated game, we find that persistent spiteful strategies, which choose the same action as the own previous action, are favored by natural selection. Altruism and spite differ concerning whether retaliatory or anti-retaliatory strategies are favored by natural selection; however, they are identical concerning whether persistent strategies are favored by natural selection.

An evolutionary game to describe doping dynamics.

The objective of this research is to delve deeply into the complex dynamics of doping in various sports disciplines, seeking to uncover the underlying mechanisms that contribute to its proliferation. Our approach involves employing ecological and biological models in conjunction with evolutionary game theory, an original aspect of this study. These models will be instrumental in simulating and understanding the intricate interactions and competitive strategies that drive athletes toward doping. The study seeks to propose effective and efficient policies and measures that can be implemented to combat the spread of doping and to identify innovative approaches that could be more effective at deterring athletes from doping, thereby ensuring a fair and level playing field in competitive sports.

An Underwater Source Location Privacy Protection Scheme Based on Game Theory in a Multi-Attacker Cooperation Scenario.

Ensuring source location privacy is crucial for the security of underwater acoustic sensor networks amid the growing use of marine environmental monitoring. However, the traditional source location privacy scheme overlooks multi-attacker cooperation strategies and also has the problem of high communication overhead. This paper addresses the aforementioned limitations by proposing an underwater source location privacy protection scheme based on game theory under the scenario of multiple cooperating attackers (SLP-MACGT). First, a transformation method of a virtual coordinate system is proposed to conceal the real position of nodes to a certain extent. Second, through using the relay node selection strategy, the diversity of transmission paths is increased, passive attacks by adversaries are resisted, and the privacy of source nodes is protected. Additionally, a secure data transmission technique utilizing fountain codes is employed to resist active attacks by adversaries, ensuring data integrity and enhancing data transmission stability. Finally, Nash equilibrium could be achieved after the multi-round evolutionary game theory of source node and multiple attackers adopting their respective strategies. Simulation experiments and performance evaluation verify the effectiveness and reliability of SLP-MACGT regarding aspects of the packet forwarding success rate, security time, delay and energy consumption: the packet delivery rate average increases by 30%, security time is extended by at least 85%, and the delay is reduced by at least 90% compared with SSLP, PP-LSPP, and MRGSLP.

Research on multilateral collaboration strategies in agricultural seed quality assurance.

Seeds, as the initial products in agricultural systems, play a pivotal role in ensuring quality, fundamental to national food security and sustainable agricultural development. This study introduces a concept integrating public governance and evolutionary game theory to construct a quadripartite evolutionary game model involving seed companies, certification agencies, farmers, and governmental departments. It considers the strategic choices of these stakeholders under varying economic motivations and market mechanisms, as well as the influence of external regulation and incentives on game strategies. The existence conditions for evolutionarily stable strategy combinations are determined using the Lyapunov first method, and MATLAB is employed for numerical simulation analysis to validate the game analysis under initial conditions. The simulation results reveal two potential equilibrium points corresponding to different strategic choices among stakeholders. The study finds that producing high-quality seeds and the refusal of certification agencies to engage in rent-seeking are crucial for ensuring seed quality. Additionally, the cost-benefit ratio of seed companies, the speculative cost of certification agencies, and the rights-protection cost of farmers are key determinants in the evolution of seed quality assurance strategies. This research also holds practical significance in enhancing seed quality assurance mechanisms and fostering sustainable development in agriculture.

Evolution of Cooperation in Spatio-Temporal Evolutionary Games with Public Goods Feedback.

In biology, evolutionary game-theoretical models often arise in which players' strategies impact the state of the environment, driving feedback between strategy and the surroundings. In this case, cooperative interactions can be applied to studying ecological systems, animal or microorganism populations, and cells producing or actively extracting a growth resource from their environment. We consider the framework of eco-evolutionary game theory with replicator dynamics and growth-limiting public goods extracted by population members from some external source. It is known that the two sub-populations of cooperators and defectors can develop spatio-temporal patterns that enable long-term coexistence in the shared environment. To investigate this phenomenon and unveil the mechanisms that sustain cooperation, we analyze two eco-evolutionary models: a well-mixed environment and a heterogeneous model with spatial diffusion. In the latter, we integrate spatial diffusion into replicator dynamics. Our findings reveal rich strategy dynamics, including bistability and bifurcations, in the temporal system and spatial stability, as well as Turing instability, Turing-Hopf bifurcations, and chaos in the diffusion system. The results indicate that effective mechanisms to promote cooperation include increasing the player density, decreasing the relative timescale, controlling the density of initial cooperators, improving the diffusion rate of the public goods, lowering the diffusion rate of the cooperators, and enhancing the payoffs to the cooperators. We provide the conditions for the existence, stability, and occurrence of bifurcations in both systems. Our analysis can be applied to dynamic phenomena in fields as diverse as human decision-making, microorganism growth factors secretion, and group hunting.

The Unification of Evolutionary Dynamics through the Bayesian Decay Factor in a Game on a Graph.

We unify evolutionary dynamics on graphs in strategic uncertainty through a decaying Bayesian update. Our analysis focuses on the Price theorem of selection, which governs replicator(-mutator) dynamics, based on a stratified interaction mechanism and a composite strategy update rule. Our findings suggest that the replication of a certain mutation in a strategy, leading to a shift from competition to cooperation in a well-mixed population, is equivalent to the replication of a strategy in a Bayesian-structured population without any mutation. Likewise, the replication of a strategy in a Bayesian-structured population with a certain mutation, resulting in a move from competition to cooperation, is equivalent to the replication of a strategy in a well-mixed population without any mutation. This equivalence holds when the transition rate from competition to cooperation is equal to the relative strength of selection acting on either competition or cooperation in relation to the selection differential between cooperators and competitors. Our research allows us to identify situations where cooperation is more likely, irrespective of the specific payoff levels. This approach provides new perspectives into the intended purpose of Price's equation, which was initially not designed for this type of analysis.