Stability of pairwise social dilemma games: Destructive agents, constructive agents, and their joint effects.

Destructive agents, who opt out of the game and indiscriminately harm others, paradoxically foster cooperation, representing an intriguing variant of the voluntary participation strategy. Yet, their impact on cooperation remains inadequately understood, particularly in the context of pairwise social dilemma games and in comparison to their counterparts, constructive agents, who opt out of the game but indiscriminately benefit others. Furthermore, little is known about the combined effects of both agent types on cooperation dynamics. Using replicator dynamics in infinite and well-mixed populations, we find that contrary to their role in facilitating cooperation in multiplayer games, destructive agents fail to encourage cooperation in pairwise social dilemmas. Instead, they replace defection in the prisoners' dilemma and stag-hunt games. Similarly, in the chicken game, they can destabilize or replace the mixed equilibrium of cooperation and defection, undermining cooperation in the harmony (trivial) game. Conversely, constructive agents, when their payoffs exceed their contributions to opponents, can exhibit effects similar to destructive agents. However, if their payoffs are lower, while they destabilize defection in prisoners' dilemma and stag-hunt games, they do not disrupt the cooperation equilibrium in harmony games and have a negligible impact on the coexistence of cooperation in chicken games. The combination of destructive and constructive agents does not facilitate cooperation, but instead generates complex evolutionary dynamics, including bistable, tristable, and quadstable states, with outcomes contingent on their relative payoffs and game types. These results, taken together, enhance our understanding of the impact of the voluntary participation mechanism on cooperation, contributing to a more comprehensive understanding of its influence.

Hybrid reward-punishment in feedback-evolving game for common resource governance.

How to maintain the sustainability of common resources is a persistent challenge, as overexploiters often undermine collective efforts by prioritizing personal gain. To mitigate the overexploitation of resources by violators, previous theoretical studies have revealed that the introduction of additional incentives, whether to reward rule-abiding cooperators or to punish those who overexploit, can be beneficial for the sustainability of common resources when the resource growth rate is not particularly low. However, these studies have typically considered rewarding and punishing in isolation, thus overlooking the role of their combination in common resource governance. Here, we introduce a hybrid incentive strategy based on reward and punishment within a feedback-evolving game, in which there is a complex interaction between human decision making and resource quantity. Our coevolutionary dynamics reveal that resources will be depleted entirely, even with cooperative strategies for prudent exploitation, when resource growth is slow. When the rate of resource growth is not particularly low, we find that the coupled system can generate a state where resource sustainability and cooperation can be maintained. Furthermore, when the rate of resource growth is moderate, we find that achieving this state cannot simply allocate all incentive budgets to reward. In addition, the increase in per capita incentives significantly promotes the stability of this state.

Four-party evolutionary game analysis of enterprise environmental behavior.

With the implementation of the "Rural Revitalization Strategy" in China, it is common for enterprises to go to the countryside to develop business. However, enterprises often neglect the local environmental protection in rural areas while developing the economy to pursue profits. As the end of the national administrative system and the villagers' autonomous organization, the village committee needs to participate in monitoring enterprises' environmental behavior. With this in mind, this paper builds a game model of enterprises, grass-roots governments, farmers, and village committees and analyzes the impact of village committees, grass-roots governments, and farmers on enterprise environmental behavior. The conclusions are as follows: (i) it is difficult for the village committee to promote the positive environmental behavior of enterprises, which needs the supervision of the grass-roots government; (ii) Improving the coordination ability of village committees is conducive to reducing the burden of government supervision; (iii) Farmers' awareness of environmental protection can affect the environmental behavior of enterprises through the rights protection mechanism and reputation mechanism.

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

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

Evolutionary game and simulation study of public transport under government incentive and punishment mechanism.

Public transport plays an indispensable role in the whole public transport system. This paper makes an in-depth study on how public transport can provide passengers with higher service quality while meeting the needs of passengers. In order to achieve this research goal, this paper organically incorporates the three key subjects of government supervision, public transport and passengers into the research framework. Evolutionary game theory is used to construct the corresponding research model. It has been found that the decision-making behaviours of government regulators, public transport and passengers are intricately intertwined to influence each other in the evolutionary process. It is particularly noteworthy that the incentive or punishment measures adopted by the government have a great impact on the quality of public transport services. In addition, timely supervision and inspection of government regulatory authorities by higher authorities proved to be crucial for buses to provide stable and high-quality services. This study reveals the mechanisms of interaction between different subjects in the public transport system, particularly the government-guided incentive measures and supervision mechanism to promote the overall service level. To further support the research conclusions, this paper carries on the simulation analysis, and puts forward the countermeasures and suggestions for the bus to provide high-quality service according to the simulation results. These recommendations will help guide the government, public transport and passengers to make better decisions in the synergistic development process, thereby improving the overall level of service.

Catalytic evolution of cooperation in a population with behavioral bimodality.

The remarkable adaptability of humans in response to complex environments is often demonstrated by the context-dependent adoption of different behavioral modes. However, the existing game-theoretic studies mostly focus on the single-mode assumption, and the impact of this behavioral multimodality on the evolution of cooperation remains largely unknown. Here, we study how cooperation evolves in a population with two behavioral modes. Specifically, we incorporate Q-learning and Tit-for-Tat (TFT) rules into our toy model and investigate the impact of the mode mixture on the evolution of cooperation. While players in a Q-learning mode aim to maximize their accumulated payoffs, players within a TFT mode repeat what their neighbors have done to them. In a structured mixing implementation where the updating rule is fixed for each individual, we find that the mode mixture greatly promotes the overall cooperation prevalence. The promotion is even more significant in the probabilistic mixing, where players randomly select one of the two rules at each step. Finally, this promotion is robust when players adaptively choose the two modes by a real-time comparison. In all three scenarios, players within the Q-learning mode act as catalyzers that turn the TFT players to be more cooperative and as a result drive the whole population to be highly cooperative. The analysis of Q-tables explains the underlying mechanism of cooperation promotion, which captures the "psychological evolution" in the players' minds. Our study indicates that the variety of behavioral modes is non-negligible and could be crucial to clarify the emergence of cooperation in the real world.

The effects of herding and dispersal behaviour on the evolution of cooperation on complete networks.

Evolutionary graph theory has considerably advanced the process of modelling the evolution of structured populations, which models the interactions between individuals as pairwise contests. In recent years, these classical evolution models have been extended to incorporate more realistic features, e.g. multiplayer games. A recent series of papers have developed a new evolutionary framework including structure, multiplayer interactions, evolutionary dynamics, and movement. However, so far, the developed models have mainly considered independent movement without coordinated behaviour. Although the theory underlying the framework has been developed and explored in various directions, several movement mechanisms have been produced which characterise coordinated movement, for example, herding. By embedding these newly constructed movement distributions, within the evolutionary setting of the framework, we demonstrate that certain levels of aggregation and dispersal benefit specific types of individuals. Moreover, by extending existing parameters within the framework, we are not only able to develop a general process of embedding any of the considered movement distributions into the evolutionary setting on complete graphs but also analytically produce the probability of fixation of a mutant on a complete N-sized network, for the multiplayer Public Goods and Hawk-Dove games. Also, by applying weak selection methods, we extended existing previous analyses on the pairwise Hawk-Dove Game to encompass the multiplayer version considered in this paper. By producing neutrality and equilibrium conditions, we show that hawks generally do worse in our models due to the multiplayer nature of the interactions.

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

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

Recent achievements in nonlinear dynamics, synchronization, and networks.

This Focus Issue covers recent developments in the broad areas of nonlinear dynamics, synchronization, and emergent behavior in dynamical networks. It targets current progress on issues such as time series analysis and data-driven modeling from real data such as climate, brain, and social dynamics. Predicting and detecting early warning signals of extreme climate conditions, epileptic seizures, or other catastrophic conditions are the primary tasks from real or experimental data. Exploring machine-based learning from real data for the purpose of modeling and prediction is an emerging area. Application of the evolutionary game theory in biological systems (eco-evolutionary game theory) is a developing direction for future research for the purpose of understanding the interactions between species. Recent progress of research on bifurcations, time series analysis, control, and time-delay systems is also discussed.

Clarifying social norms which have robustness against reputation costs and defector invasion in indirect reciprocity.

The evolution of cooperation through indirect reciprocity is a pivotal mechanism for sustaining large-scale societies. Because third parties return cooperative behaviour in indirect reciprocity, reputations that assess and share these third parties' behaviour play an essential role. Studies on indirect reciprocity have predominantly focused on the costs associated with cooperative behaviour, overlooking the costs tied to the mechanisms underpinning reputation sharing. Here, we explore the robustness of social norms necessary to secure the stability of indirect reciprocity, considering both the costs of reputation and the resilience against perfect defectors. Firstly, our results replicate that only eight social norms, known as the 'leading eight,' can establish a cooperative regime. Secondly, we reveal the robustness of these norms against reputation costs and perfect defectors. Our analysis identifies four norms that exhibit resilience in the presence of defectors due to their neutral stance on justified defection and another four that demonstrate robustness against reputation costs through their negative evaluation of unjustified cooperation. The study underscores the need to further research how reputational information is shared within societies to promote cooperation in diverse and complex environments.

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

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

Evolutionary branching in multi-level selection models.

We study a model of group-structured populations featuring individual-level birth and death events, and group-level fission and extinction events. Individuals play games within their groups, while groups play games against other groups. Payoffs from individual-level games affect birth rates of individuals, and payoffs from group-level games affect group extinction rates. We focus on the evolutionary dynamics of continuous traits with particular emphasis on the phenomenon of evolutionary diversification. Specifically, we consider two-level processes in which individuals and groups play continuous snowdrift or prisoner's dilemma games. Individual game strategies evolve due to selection pressure from both the individual and group level interactions. The resulting evolutionary dynamics turns out to be very complex, including branching and type-diversification at one level or the other. We observe that a weaker selection pressure at the individual level results in more adaptable groups and sometimes group-level branching. Stronger individual-level selection leads to more effective adaptation within each group while preventing the groups from adapting according to the group-level games.

Hypernetwork modeling and topology of high-order interactions for complex systems.

Interactions among the underlying agents of a complex system are not only limited to dyads but can also occur in larger groups. Currently, no generic model has been developed to capture high-order interactions (HOI), which, along with pairwise interactions, portray a detailed landscape of complex systems. Here, we integrate evolutionary game theory and behavioral ecology into a unified statistical mechanics framework, allowing all agents (modeled as nodes) and their bidirectional, signed, and weighted interactions at various orders (modeled as links or hyperlinks) to be coded into hypernetworks. Such hypernetworks can distinguish between how pairwise interactions modulate a third agent (active HOI) and how the altered state of each agent in turn governs interactions between other agents (passive HOI). The simultaneous occurrence of active and passive HOI can drive complex systems to evolve at multiple time and space scales. We apply the model to reconstruct a hypernetwork of hexa-species microbial communities, and by dissecting the topological architecture of the hypernetwork using GLMY homology theory, we find distinct roles of pairwise interactions and HOI in shaping community behavior and dynamics. The statistical relevance of the hypernetwork model is validated using a series of in vitro mono-, co-, and tricultural experiments based on three bacterial species.

Research on different modes of energy conservation and emission reduction: A differential game model based on carbon trading perspective.

In recent years, due to global climate change, increasing resource scarcity, and environmental constraints, countries have prioritized energy conservation and emissions reduction. However, enterprises are primarily responsible for energy saving and emissions reduction. To encourage industrial enterprises to engage in energy conservation and emissions reduction, high-carbon enterprises must purchase carbon emission rights from low-carbon counterparts. Common modes of energy conservation and emission reduction of industrial enterprises include reducing production scale, improving energy utilization efficiency, and expanding renewable energy. This article constructs three differential game models to identify the applicable scope of various energy conservation and emission reduction strategies, comparing and analyzing the equilibrium results. The study concludes that when the cost of changing the production mode and the income obtained from the production of unit product is large, the low-carbon enterprise can obtain the maximum benefit by reducing the production scale mode. Otherwise, low carbon enterprises can be maximized through improving energy efficiency mode. For both low-carbon and high-carbon enterprises, reducing production scale is the fastest way to enhance efficiency when the costs of energy conservation and emission reduction are substantial.

Advancing sentiment classification through a population game model approach.

Computational Sentiment Analysis involves the automation of human emotion comprehension by categorizing sentiments as positive, negative, or neutral. In the contemporary digital environment, the extensive volume of social media content presents significant challenges for manual analysis, thereby necessitating the development and implementation of automated analytical tools. To address the limitations of existing techniques, which heavily rely on machine learning and extensive dataset pre-training, we propose an innovative unsupervised approach for sentiment classification. This novel methodology is grounded in game theory concepts, particularly the population game model, offering a promising solution by circumventing the need for extensive training procedures. We extract two textual features from review comments, namely context score and emotion score. Leveraging lexicon databases and numeric scores, this cognitive mathematical framework is language-independent. Competitive results are demonstrated across various domains (hotels, restaurants, electronic devices, etc.), and the efficacy of the proposed work is validated in two languages (English and Hindi). The highest accuracy recorded for the English domain dataset is 89%, while electronic Hindi reviews attain an 84% accuracy rate. The proposed model exhibits domain and language independence, validated through statistical analyses confirming the significance of the findings. The framework demonstrates noteworthy rationality and coherence in its outcomes.

Cooperation dynamics in multi-issue repeated social dilemma games with correlated strategy.

In the real world, individuals are often involved in collaboration on multiple issues, and these issues may interact with each other. Given the complexity of the interaction, we establish a multi-issue repeated game model, in which individuals participate in multiple social dilemma games simultaneously and repeatedly, and strategies in different issue games are correlated and reactive. We explore the cooperation dynamics of strategies in the population from a multiobjective perspective, in which an individual's preference for each issue is described by a weight vector, and heterogeneous preferences of individuals in the population are also considered. Through simulations on two-issue games, we find that compared to the uncorrelated case, the correlated strategy can significantly promote cooperation in both games regardless of which issue players prefer. Under the condition of homogeneous preference, an increase in the payoff weight of a given issue decreases the level of cooperation in that issue, and the optimal condition to sustain cooperation to the maximum extent is when the payoff weights of all issues are equal. Moreover, under the condition of heterogeneous preference, there exists an optimal proportion of players with different preferences under which the cooperation rate can reach its highest level in the population. This work highlights individual trade-offs on different issues when engaging in multiple games simultaneously and further enriches the research of evolutionary games from a multiobjective and correlated strategy perspective.

Simulating pedestrian avoidance: The human-zombie game.

This study introduces a simulated active matter system, applying the pedestrian collision avoidance paradigm, which involves dynamically adjusting the desired velocity. We present a human-zombie game set within a closed geometry, combining predator-prey behavior with a one-way contagion process that transforms prey into predators. The system demonstrates varied responses in our implemented model: with agents having the same maximum speeds, a single zombie always captures a human, whereas two zombies never capture a single human agent. As the number of human agents increases, observables such as the final fraction of zombie agents and total conversion times exhibit significant changes in the system's behavior at intermediate density values. Most notably, there is evidence of a first-order phase transition when analyzing the mean population speed as an order parameter.

Impact of environmental stochastic fluctuations on the evolutionary stability of imitation dynamics.

To show the impact of environmental noise on imitation dynamics, the stochastic stability and stochastic evolutionary stability of a discrete-time imitation dynamics with random payoffs are studied in this paper. Based on the stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model, we extend the concept of stochastic evolutionary stability to the stochastic imitation dynamics, which is defined as a strategy such that, if all the members of the population adopt it, then the probability for any mutant strategy to invade the population successfully under the influence of natural selection is arbitrarily low. Our main results show clearly that the stochastic evolutionary stability of the system depends only on the properties of the mean matrix of the random payoff matrix and is independent of the randomness of the random payoff matrix. Moreover, as two examples, we show also that under the framework of stochastic imitation dynamics, the noise intensity affects the evolution of cooperative behavior in a stochastic prisoner's dilemma game and the system's nonlinear dynamic behavior.

GPT-3.5 altruistic advice is sensitive to reciprocal concerns but not to strategic risk.

Pre-trained large language models (LLMs) have garnered significant attention for their ability to generate human-like textand responses across various domains. This study delves into examines the social and strategic behavior of the commonly used LLM GPT-3.5 by investigating its suggestions in well-established behavioral economics paradigms. Specifically, we focus on socialpreferences, including altruism, reciprocity, and fairness, in the context of two classic economic games: the Dictator Game(DG) and the Ultimatum Game (UG). Our research aims to answer three overarching questions: (1) To what extent do GPT-3.5suggestions reflect human social preferences? (2) How do socio-demographic features of the advisee and (3) technicalparameters of the model influence the suggestions of GPT-3.5? We present detailed empirical evidence from extensiveexperiments with GPT-3.5, analyzing its responses to various game scenarios while manipulating the demographics of theadvisee and the model temperature. Our findings reveal that, in the DG Dictator Game, model suggestions are more altruistic than in humans.We further show that it also picks up on more subtle aspects of human social preferences: fairness and reciprocity. Thisresearch contributes to the ongoing exploration of AI-driven systems' alignment with human behavior and social norms,providing valuable insights into the behavior of pre-trained LLMs and their implications for human-AI interactions.Additionally, our study offers a methodological benchmark for future research examining human-like characteristics andbehaviors in language models.

How to design subsidy policies to better encourage travelers to use car-sharing instead of private cars? An evolutionary game study.

Car-sharing is a travel mode that can serve as an alternative to private cars, helping to reduce urban pollution. However, currently, there is a low willingness among travelers to use car-sharing, which is reflected in both low market penetration and user frequency. Therefore, it is essential for the government to encourage the use of car-sharing by providing subsidies. To better encourage the usage of car-sharing, this paper applies a two-fold evolutionary game model involving travelers and the government to explore the impact of subsidies on travelers' choices, and the factors that could affect the subsidies' efficiency. A simulation, using data from Beijing, was conducted to determine the implications of subsidy policies. The results show that a mileage-based subsidy and a fixed subsidy are applicable to travel of high and low mileages respectively, and under both subsidy modes, subsidies for trips with short duration or short pick-up and return time are more effective. Furthermore, we find that the efficiency of subsidies increases as the scale of car-sharing users, demand elasticity, or total number of travelers increases. Additionally, the subsidy levels should be lower than the environmental benefits of car-sharing but higher than the difference in travel costs between private cars and car-sharing. Future work will involve other game players such as car-sharing operators in order to draw deeper conclusions, and will involve the collection of data from more countries and cities to develop the robustness of the conclusions.