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Exploring the emergence of cooperation in the populations of self-interested individuals is of huge challenge. Evolutionary game theory has been utilized to investigate the evolution of cooperation. In recent years, many researchers have paid massive attention on the evolution of cooperative behavior from the perspective of multiple games, especially the transition of games. Nevertheless, not only are the current interactive actions crucial, but also the historical interactive experience is fateful. Motivated by this, the persistence-based game transition mechanism is proposed and introduced to investigate the evolution of cooperation, where both the current pairwise strategies and the persistence of the pairwise strategies determine the game played in the next time step. Through analyzing the evolutionary results of strategies and games, we find that the cooperation can be facilitated by the enhanced network reciprocity as the persistence-based game transition makes mutual cooperators play games with weak dilemma more persistently. • A persistence-based game transition is proposed in multi-games. • In our model, both pairwise interactive strategies and the persistence of pairwise strategies determine the game transition. • The persistence-based game transition can facilitate cooperation through enhancing network reciprocity. [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]

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]

• 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]