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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]

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]

• 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]

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]