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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]

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]