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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]

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 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]