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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]

• 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]

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]