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How to effectively maintain costly intra-group cooperation has always been a topic of great concern in society. As we all know, inter-group competition is a constructive way to promote intra-group cooperation. Previous inter-group competition mechanisms are primarily based on the total contribution value of all individuals in the group in the current round, which ignore the historical behavior of the group and its members. For comparison, we argue that the introduction of collective reputation which reflects not only the total contribution of the groups in the current round but also the group's historical behavior is necessary for the construction of an inter-group competition model. Furthermore, an excellent collective reputation can help the group obtain more high-quality resources and help the group stand out from the competition. To this end, we introduce a new mechanism of inter-group transfer payment driven by collective reputation and construct a public goods game (PGG) model of inter-group competition to study the dynamic behavior of intra-group cooperation evolution. Two parameters, the proportion of accepted groups a and the proportion of transferred groups b , are introduced. The simulation results suggest that the effectiveness of this model in promoting cooperation depends largely on the joint settings of a and b. And in most cases, the combination of small a and medium b plays the significant role. [ABSTRACT FROM AUTHOR]

The interaction radius is crucial in spatial evolutionary games, but previous studies have overlooked the dynamic nature of individuals adjusting their interaction circles based on their states. This manuscript investigates the impact of dynamic changes in interaction radius on cooperation, specifically examining the influence of emotion-induced heterogeneity. Individuals are categorized into non-competitive and competitive groups, highlighting their differing emotional responses to game outcomes. By affecting the dynamics of their interaction radius, emotions play a role in cooperation. Specifically, adjusting the interaction radius based on emotions effectively enhances cooperation by enabling individuals to secure survival opportunities through distinct evolutionary pathways. The study also explores the influence of unit emotional value size and unit game initiation cost on cooperation evolution, shedding light on their effects. Furthermore, the research examines the non-linear relationship between the maximum interaction radius and cooperation. By considering the interplay of emotions and the dynamics of interaction radius, this research advances the understanding of cooperation in evolutionary games and emphasizes the significance of individual-level adjustments in interaction radius. • Exploring the effects of emotion-based interaction range heterogeneity on cooperation in a spatial public goods game. • The model investigates the impact of dynamic changes in interaction radius on cooperation, specifically examining the influence of emotion-induced heterogeneity. • The unit emotional value and the unit organizational costs have a non-negligible role for cooperation. [ABSTRACT FROM AUTHOR]

Previous experience suggests that prior agreement (a mechanism to test how strongly peers are committed to a common goal) and posterior compensation (a way to compensate cooperators by punishing defectors who violate their commitments) together contribute to the flourishing of cooperation. Far less is known, however, how the determination of the optimal threshold for prior agreement in force and the posterior compensation affect collaboration, and the relevance of different strategies. Here, in the context of public goods games and using an evolutionary game theory model, we investigate the evolution of cooperation and the relevance of different strategies by introducing prior agreements and posterior compensation in structured populations. Analytical results show that posterior compensation does not always promote cooperation and that there are sudden increases and decreases in the first-order phase transition. Interestingly, prior agreements without posterior compensation can also effectively restrain defectors, with cooperation abundance remaining at a high level. Furthermore, the threshold of effective agreement has nonlinear effects on cooperation, with cooperation abundance peaking at intermediate thresholds under specific parameters. • The prior agreements and posterior compensation are introduced in network reciprocity. • The model aims to determine the optimal threshold of agreements and the correlation between different strategies. • The effects of posterior compensation and the threshold of agreements in force on the proportion of cooperation are not linear. [ABSTRACT FROM AUTHOR]

Identifying the most influential individuals in structured populations is an important research topic throughout network science. Previous studies, whether identifying the initial cooperators in a network that can lead to the spread of cooperation or assessing the chances that an intrusive defector may lead to the collapse of cooperation, have assumed that all individual attributes are homogeneous. However, heterogeneity among humans is widespread and can sometimes affect cooperation and welfare. For example, the layout of non-cooperative individuals in cooperative individuals inhibits the evolution of cooperation. Therefore, specifying the heterogeneity of individuals and studying the effect of their initial position on cooperation is the focus of our attention. Here we hypothesize that individuals in the network are divided into cooperative and non-cooperative individuals according to the heterogeneity of social value orientations, and we investigate the effects of the initial position of non-cooperative individuals on cooperation by adding them through different ranking rules to the network composed of cooperative individuals. We investigate separately the effects of the proportion of non-cooperative individuals, the proportion of initial cooperators of different types of individuals and different game scenarios on cooperation under different ranking rules. The results show that the addition of non-cooperative individuals to cooperative populations can effectively hinder the spread of cooperation. We also find that the proportion of initial cooperators for different types of individuals and the effects of different game types on population evolution also differ significantly under different ranking rules. • Identifying how the most influential individuals have an impact on the evolution of cooperation under different ranking rules. • Our model classifies individuals into non-cooperative and cooperative individuals through the heterogeneity of their social value orientations, and thus investigates the impact of strategically positioned non-cooperative individuals who tend to defect. • Non-cooperative individuals block cooperation between cooperative individuals; the initial proportion of different types of individuals as well as different game scenarios also have a significant effect on the evolution of cooperation. [ABSTRACT FROM AUTHOR]

Exploring the emergence and maintenance of cooperation in social dilemma is valuable and it arises considerable concerns of many researchers. In this paper, we propose a mechanism to promote cooperation, called benefit community, in which cooperators linking together form a common benefit community and all their payoffs obtained from game are divided coequally. The robustness of conclusions is tested for the PDG (prisoners' dilemma game) on square lattice and WS small world network. We find that cooperation can be promoted by this typical mechanism, especially, it can diffuse and prevail more easily and rapidly on the WS small world network than it on the square lattice, even if a big temptation to defect b. Our research provides a feasible direction to resolve the social dilemma. [ABSTRACT FROM AUTHOR]

In peer-to-peer interaction, people have conditions to adopt different strategies against different opponents, which is called interactive diversity. Recently, the evolution of cooperation under interactive diversity has attracted much attention, but the potential cost of maintaining interactive diversity is rarely considered. Actually, individuals may need to frequently switch their strategies between interactions with different opponents. If strategy switching is costly, individuals are likely to prefer strategies that can be maintained to strategies that require frequent changes. In other words, individuals may have behavioral inertia in their interactions with different opponents. Although some studies have found that appropriate strategy switching costs or inertia can promote cooperation under interactive identity, their role under interactive diversity remains to be further discussed. The main reason is that strategy switching costs may restrain the diversity of strategies, and the differentiation of strategies is exactly the key to cooperation under interactive diversity. In this work, we are devoted to reveal the impact of strategy switching costs on the evolution of cooperation under interactive diversity. Simulation results show that appropriate strategy switching costs are also positive under interactive diversity, but higher strategy switching costs play completely different roles in different networks. Especially, cooperation in lattice network sometimes shows a non-monotonic dependence of "first increasing, second decreasing and then increasing again" on unit switching cost. These findings are of great significance for understanding the emergence of cooperation in paired interaction under interactive diversity. • We study the effect of strategy switching costs under interactive diversity. • Small switching costs can promote cooperation on multiple networks. • Medium switching costs may hinder cooperation on lattice network. • Excessive switching costs in ER network and BA network are unbearable. • The reasons for the phenomenon differences across networks are analyzed. [ABSTRACT FROM AUTHOR]

In repeated games, historical interactions lead to varying environment. Among existing studies, the variation of environment or game is basically considered from the perspective of nodes, while in pairwise game, it is more reasonable to consider the interactive environment from the perspective of edges. In addition, since historical interactive experience of pairwise players has an impact on the current interactive environment, the duration of pairwise strategies produces differentiated results. Therefore, we consider the persistence-dependent dynamic interactive environment where the persistence of pairwise strategy affects the weight between two interacting players, and the game resource of interactive environment is influenced by varying weight. The results suggest that the introduction of persistence-dependent dynamic interactive environment can effectively enhance cooperation, and a larger weight increment of CD link generates a higher cooperation level as it indicates that the reward for cooperative behavior is significant, although a single cooperator for the pairwise interacting players. • We introduce the persistence-dependent dynamic interactive environment in prisoner's dilemma game. • An intermediate variable, weight, is introduced and influenced by the strategy persistence of pairwise players. • The fluctuation scale of weight is dependent on distinct kinds of edge links, and a parameter η for CD link is introduced. • The variation of weight determines the changing resources for the interactive environment. • Our new model can boost cooperation significantly, especially for the larger η. [ABSTRACT FROM AUTHOR]

Public resource redistribution is an important means of social income regulation, which maintains social income equality by transferring payoffs to low-income groups, usually in the form of taxes and social services. Originally studied as a means of maintaining social equality, redistribution has also been used to address social dilemmas through evolutionary game theory in recent years. However, the definition of low-income groups in previous studies is not comprehensive. They are used to studying the inequality generated by participants during the game but ignore the inequality caused by initial endowment differences. At the same time, is it beneficial to the whole that redistribution requires the rich to subsidize the poor, but leads the rich to choose defection (tax evasion, etc.)? How should the redistribution mechanism work to reduce inequality while facilitating the spread of altruistic behavior? To explore whether the redistribution mechanism can reach a balance between promoting cooperation and maintaining equality of payoffs, we develop a generic public resource redistribution framework based on heterogeneous populations by a spatial public goods game model. We control redistribution preferences for willingness to cooperate and initial endowments by parameters α and β. With a heterogeneous population, we find that helping the poor through redistribution mechanisms does not have significant positive effects and may even result in exploitation of the rich; focusing on participants' willingness to cooperate rather than total investment can promote cooperation, enhance overall payoffs and reduce inequality. • A generic redistribution framework based on heterogeneous populations has been proposed. • Helping the poor does not always have a positive effect. • Focusing on willingness to cooperate can promote cooperation and reduce inequality. [ABSTRACT FROM AUTHOR]

Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Grasping the force that fosters and sustains cooperative behaviors is thus of central importance for the understandings of how companies develop and how societies thrive. In this paper, by means of evolutionary game theory, we refresh the strategy updating rule to be matched with a more realistic scenario where individuals choose someone excellent as the role model and improve themselves continuously to narrow the gap. Under the force of role model, individuals adjust their instantaneous strategy with the increment δ in the next continuous M time steps. And a new role model needs to be selected unless its payoff is more than the focal player's. The computer simulation results illustrate that the self-improvement driven by role model facilitate group cooperation significantly, and the slow but persistent self-improvement performs better. Therefore, in order to achieve higher enterprise performance and build a more harmonious society, managers and government officials should spare no effort to encourage people to keep improving themselves to keep up with their role models. • A new strategy updating rule, self-improvement driven by role model updating rule is proposed. • Players make self-improvement according to the persistent choosing reference roles. • The simulation results show that a slow but persistent self-improvemnet enhances cooperation markedly. [ABSTRACT FROM AUTHOR]

In previous studies of evolutionary games, players change reference objects at each time step. However, in real life, many people tend to consistently imitate outstanding role models instead of changing reference objects frequently. From this, a persistent imitation rule is proposed. In detail, a persistent imitator will persist in imitating his or her reference object until the wealth exceeds that of the reference object or the duration of continuous imitation exceeds a specific value. Furthermore, to reflect inter-individual differences, we divide the players into two categories, persistent imitators and random imitators. The simulation suggests that the presence of a high proportion of persistent imitators has a significant effect on the development of cooperation, and the level of cooperation increases as the maximum duration of imitation increases. However, when the proportion of persistent imitators or the maximum duration of imitation is small, the promotion effect on cooperation is not obvious. • The persistent imitation of reference objects is proposed. • Persistent imitators refresh the role model if their payoff exceeds the last one's. • After the maximum duration, the persistent imitator chooses a new reference object. • The presence of persistent imitators can effectively facilitate cooperation. [ABSTRACT FROM AUTHOR]

In previous studies about heterogeneous investment, many researchers only focus on the monodirectional effect of reputation, but ignore the reversed influence about the heterogeneity of reputation fluctuation driven by investment. Given this, considering the interplay between reputation and heterogeneous investment, we explore the evolution of cooperation in public goods game. In detail, each player's reputation situations in different groups determine its differentiated investment amounts, and in turn, the heterogeneity of reputation fluctuation is dependent on how much it invests into each group. Furthermore, we introduce two parameters, α and β , to characterize the effect degree of investment on heterogeneous reputation fluctuation and the one of reputation on heterogeneous investment, respectively. The simulation results suggest that cooperation can be boosted to some extent, especially for the larger α and β , as they magnify the interplay of reputation and heterogeneous investment. • We introduce the interplay between reputation and heterogeneous investment in the public goods game. • Reputation effects unequal investment and heterogeneous reputation fluctuation is effected by investment in turn. • We introduce parameter α to characterize the effect degree of investment on heterogeneous reputation fluctuation. • Parameter β is presented to denote the effect degree of reputation on heterogeneous investment. • Our new model can boost cooperation significantly, especially for the larger α and β. [ABSTRACT FROM AUTHOR]

Relational diversity can be characterized by heterogeneous distributions of tie strengths in social networks and this diversity is present not only among humans, but throughout the animal world. We account for this observation by analyzing two network datasets from Facebook. We measure the strength of a tie by calculating the extent of overlap of friends between the two individuals. Based on the previous findings in human experiments, we argue that it is very unlikely that players will allocate their investments equally to their neighbors. There is a tendency that players prefer to donate more to their intimate friends. We find that if players preferentially allocate their investments to their good friends, cooperation will be promoted in PDG. We proved that the facilitation of the cooperative strategy relies mostly on the cooperative allies between best friends, resulting in the formation of cooperative clusters which are able to prevail against the defectors even when there is a large cost to cooperate. Moreover, we discover that the effect of relational diversity cannot be analyzed by adopting classical complex networks models, because neither of the artificial networks is able to produce networks with diverse distributions of tie strengths. It is of vital importance to introduce real social networks to study the influence of diverse relations especially when it comes to humans. This research proposes a brand new perspective to understand the influence of social relations on the emergence of cooperation in evolutionary prisoner’s dilemma games. [ABSTRACT FROM AUTHOR]

• A new framework of multiple public goods games considering the persistence and transition of games is proposed. • The heterogeneous public resource of public goods game evolves with the persistence and transition of games. • Our new model can promote cooperation effectively, especially under the condition with scarce resource. Many various projects may exist in an enterprise in parallel, which leads to distinct group interactions. Team members cooperate in their respective projects, and sometimes it is possible to engage in several concurrent projects. Owing to practice makes perfect, the longer the duration of members participating in an identical project is, the higher benefits will be under same contribution. However, in a fiercely competitive environment, a huge conflict of interest between groups and individuals which results in social dilemma makes projects difficult to proceed smoothly. The experience of direct reciprocity shows that repeated interactions can alleviate this problem, but most multi-person dilemma studies consider a single game scenario, and public resources remain constant. Here we introduce a general framework of multiple public goods games. Taking the public goods game with threshold into consideration, public resource evolves with the persistence and transition of games. Our results suggest although collaborators are at a disadvantage in different game scenarios, our model can still effectively promote the overall cooperation in multiple public goods games. Especially, it performs better when public resource is relative scarce. [ABSTRACT FROM AUTHOR]

• The evolution of cooperation hypothesized that individual selection is inevitable is investigated. • Distinct from the traditional models, our model studied the effects of wealth-based rule when individual selection is inevitable, where only the top V individuals with relatively high cumulative payoffs in each group can be selected for costly PGG. • The effects of participation costs on the proportion of cooperation, the proportion of different individuals, and the gap between rich and poor individuals are distinctly different under different V. Individual selection, as an effective mechanism, is often used in spatial evolutionary games to promote cooperation. Previous research assumes that, individual selection usually occurs with people who fail to meet a certain criterion. However, individual selection is usually inevitable, regardless of whether players in population cooperate or defect. This paper studies the effects of wealth-based rule in costly public goods games when individual selection is inevitable. Specifically, we assume that only the top V individuals with relatively high cumulative payoffs in each group can be selected for costly PGG. The results show that when V is large, the increase of participation cost has slight inhibitory effects on the evolution of cooperation, but it alleviates the polarization of individuals. However, when V is small, the increase of participation cost within a certain range promotes cooperation prosperity, but it also causes an increase in the proportion of polarized individuals and a widening of the wealth gap between rich and poor individuals. [ABSTRACT FROM AUTHOR]

• The evolution of cooperation hypothesized that emotion can influence one's own willingness to change strategies is investigated. • Distinct from the traditional evolutionary model, our model hypothesized that individuals are divided into two categories, namely, non-competitive individuals and competitive individuals, and their emotion is considered quantifiable and cumulative. • The existence of non-competitive individuals has a significant positive effect on the survival of cooperators, but the presence of competitive individuals also makes non-competitive individuals much less effective in promoting cooperation. • The emotional cumulative length plays a key role in promoting overall cooperation, but surprisingly, the cooperation rate of competitive individuals peaks at an intermediate value of emotional cumulative length. Emotion emerges along with individuals' interactions, and numerous experimental studies have shown that emotion plays an important role in individual decision making. However, how emotion affects the evolution of cooperation in structured population is largely unknown. Here we introduce emotion into network reciprocity, where emotion is considered quantifiable and cumulative, and then divide individuals into two types, namely non-competitive individuals whose social value orientation is mutually beneficial and competitive individuals whose social value orientation is maximizing outcomes for the self. Here, we explore the effects of the proportion of non-competitive individuals and emotional cumulative length on the evolution of cooperation. Simulation results show that the existence of non-competitive individuals promotes cooperation in the system. Furthermore, we also find that emotional cumulative length plays a key role in promoting overall cooperation, but surprisingly, the cooperation rate of competitive individuals peaks at an intermediate value of emotional cumulative length. [ABSTRACT FROM AUTHOR]

Affected by geographical or social factors, human communities are organized with changeless groups for teamwork. Within groups, defection dominates because the payoffs of defectors are often higher than those of cooperators; among groups, higher cooperation level makes individuals wealthier. For the previous mechanism of evolutionary dynamics leading individuals to imitate the rich in their groups, defective strategy evolves. However, individuals who belong to different groups and have no direct interaction of interests actually could influence each other. Due to the similarity of environment, the strategies among groups have the channel and necessity of dissemination. To this end, we propose an evolutionary game model with inter-group selection of strategy. By simulations, the effects of groups' selection preference, group size, multiplier factor, imitation intensity and competition among groups on cooperative evolution in populations are studied. We find that when the group makes selection without preference, the intensity of the choice positively affects the level of cooperation; the strategy selection with preference can effectively increase the group cooperation rate. • An evolutionary game model considering inter-group selection of strategy is proposed. • A player in one group can imitate strategy of individuals in other groups. • The preference and other factors have been considered in evolutionary game. • Cooperation can be promoted effectively by our new mechanism. [ABSTRACT FROM AUTHOR]

• A reputation-based strategy persistence mechanism in evolutionary game is proposed. • Our mechanism illuminates that the scale of reputation fluctuation totally depends on the persistence of last strategy. • A parameter, α , illustrating the impact of strategy persistence on reputation variation, is introduced. • Cooperation can be promoted effectively by our new mechanism. Understanding the emergence and maintenance of cooperation in social dilemma has received a lot of attention. In previous research, many scholars found that the reputation mechanism can promote cooperation, and the variation of reputation is consistent. However, in reality, according to both one's current action and past experiences, every individual's impression from others is modified to varying extent everyday. In other words, the length of duration of the same performance influences the diverse scale of their own reputation fluctuation. Therefore, a reputation-based strategy persistence mechanism, in which the increment of current reputation is determined by the persistence of last strategy, is proposed. Moreover, we introduce a parameter α to illustrate the impact of strategy persistence on reputation variation. The results of simulation show that the new mechanism paves the way for cooperation in evolutionary game, and the smaller α is, the better the mechanism performs. [ABSTRACT FROM AUTHOR]

Research on cooperative evolution behavior based on memory mechanism has been a hot topic of many scholars in recent years. However, most previous studies have considered neighbors' historical payoffs when individuals choose role models whom they will learn from, but paid less attention to the stability of neighbors' strategy which indicates how frequently they change their strategies in memory length. In this paper, we study the memory length M and the strategy persistence level u of individuals and the change rate of cooperative tendency δ on the cooperative evolution under the mixed strategy of the prisoner's dilemma. Strategy persistence level is measured by the number of times which the strategy in neighbor's memory length is continuous and consistent with neighbor's current strategy, and can determine the probability that the individual learns the neighbor's strategy when updating the strategy; the change rate of cooperative tendency δ is described by the standard deviation of the normal distribution. We investigate the effects of M and δ on the evolutionary of cooperation. The results show that the persistence strategy mechanism which we proposed in the memory length can improve network reciprocity and facilitate the generation and maintenance of cooperation, the larger the memory length is, the smaller the standard deviation value is, the more conducive to cooperation. [ABSTRACT FROM AUTHOR]

This paper investigates the emergence of relationship-based cooperation by coupling two simple mechanisms into the model: tie strength based investment preference and homophily assumption. We construct the model by categorizing game participants into four types: prosocialists (players who prefers to invest in their intimate friends), antisocialists (players who prefer to invest in strangers), egoists (players who never cooperate) and altruists (players who cooperate indifferently with anyone). We show that the relationship-based cooperation (prosocialists) is favored throughout the evolution if we assume players of the same type have stronger ties than different ones. Moreover, we discover that strengthening the internal bonds within the strategic clusters further promotes the competitiveness of prosocialists and therefore facilitates the emergence of relationship-based cooperation in our proposed scenarios. The robustness of the model is also tested under different strategy updating rules and network structures. The results show that this argument is robust against the variations of initial conditions and therefore can be considered as a fundamental theoretical framework to study relationship-based cooperation in reality. [ABSTRACT FROM AUTHOR]