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Collective action, like public goods game, often requires mechanism intervention to avoid exploitation by free-riders. Reward and punishment are two widely studied solutions, but the balance of budgets and diverse behavioral motivations need further emphasis. Here, we introduce a heterogeneous distribution system based on peer rating (PRHDS), a disguised reward and punishment mechanism under budget balancing, and consider a comprehensive range of behavioral motivations. Preliminary studies show that PRHDS has the potential to promote cooperation, but is too sensitive to random exploration. This vulnerability is attributed to the exploitation of prosocial cooperators by egoistic cooperators. Afterward, we propose three punishments for minority raters and find that two monetary punishments can compensate for the above limitation. A notable finding is that the cooperation potential at medium multipliers seems to exceed that at high multipliers. In addition, our further analysis suggests that PRHDS may perform better when strategy differentiation is considered. This study reveals the possible limitations of PRHDS as a solution to collective social dilemma, and may have some enlightening significances for seeking the countermeasures. • We study a potential solution to the collective dilemma under balancing budget. • Diverse rating motivation and strategy knowability condition are considered. • The proposed mechanism is found to be too sensitive to random exploration. • We further propose remediations for stable cooperation under noise conditions. • The existence and role of interactive diversity individuals is also discussed. [ABSTRACT FROM AUTHOR]

For many years, social diversity has been recognized as one of the important factors in the emergence of cooperation. In PGG that characterizes collective social dilemmas, the difference in individual contributions to collective output usually arises from diversity of endowments and productivity, or from heterogeneous investments, but this difference may also be caused by the unequal dependence of collective output on members. In real collective actions, individuals may not contribute homogeneous currencies or goods, but instead divide labor to complete a series of tasks. Some individuals who master critical resources and skills may have a greater impact on collective output. In this work, a heterogeneous population containing elites and ordinary people plays spatial public goods game. The peculiarity is that ordinary people can make full contributions only when there are cooperative elites within the team. Otherwise, a part of the work will not be able to be carried out, and the cooperation contributions of ordinary people will be greatly reduced. Simulations under multiple social structures consistently show that the presence of a small number of elites can greatly stabilize cooperation. On the contrary, an excess of elites undermines the stable cooperative structure between elites and ordinary people. • We consider the unequal dependence of collective output on members. • A spatial public goods game involving elites and ordinary people is proposed. • There is an optimal proportion of elites that maximizes cooperation fraction. • Optimal value is not greatly affected by parameters but interactive structure. [ABSTRACT FROM AUTHOR]