The importance of cooperation is self-evident to humans, yet the existence of corruption where law violators can avoid being punished by paying bribes to corrupt law enforcers may threaten the maintenance of cooperation. Although powerful monitoring has been used to resolve such matters, existing studies show that the effects of such measures are either transient or uncertain. Thus how to efficiently control the occurrence of corruption for the emergence of cooperation remains a challenge. Here, we introduce social exclusion into the public goods game, and respectively propose three measures to control corruption, namely, the exclusion of corrupt punishers, the exclusion of corrupt defectors, and the exclusion of both corrupt punishers and corrupt defectors. Our results show that the system dynamics driven by these three measures can exhibit many interesting dynamical outcomes including the dominance of defectors, rock-scissors-paper cycle, heteroclinic cycle, or interior attractor. We further demonstrate that excluding corrupt punishers can improve the situation of corruption more efficiently than excluding corrupt defectors. In addition, excluding both corrupt defectors and corrupt punishers can more effectively promote the emergence of cooperation for a broad parameter range.

中文翻译：

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反腐败控制下腐败社会合作的演化动态

合作的重要性对人类来说是不言而喻的，但如果存在腐败，违法者可以通过贿赂腐败的执法人员来避免受到惩罚，这可能会威胁到合作的维持。尽管已使用强大的监测来解决此类问题，但现有研究表明，此类措施的影响要么是短暂的，要么是不确定的。因此，如何有效控制腐败的发生以促成合作的出现仍是一个挑战。在这里，我们将社会排斥引入公共产品博弈中，分别提出了三种控制腐败的措施，即排除腐败惩罚者、排除腐败叛逃者、排除腐败惩罚者和腐败叛逃者。我们的研究结果表明，由这三种措施驱动的系统动力学可以表现出许多有趣的动力学结果，包括叛逃者的优势、剪刀石头布循环、异宿循环或内部吸引子。我们进一步证明，排除腐败惩罚者可以比排除腐败叛逃者更有效地改善腐败状况。此外，同时排除腐败叛逃者和腐败惩罚者可以更有效地促进广泛参数范围内合作的出现。