Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China.
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China.
J Theor Biol. 2018 Jul 14;449:60-72. doi: 10.1016/j.jtbi.2018.04.018. Epub 2018 Apr 13.
Punishment is widely recognized as a potential promoter in sustaining or even enhancing public cooperation, but it meanwhile induces the problem of second-order free-riders. Particularly, recent evidence shows that costly punishment can be maintained if punishers may engage in corruption. However, how to reduce or eliminate incidents of corruption has been the enduring conundrum in human society. As power asymmetries are associated with hierarchies, we investigate how costly punishment affects the evolution of cooperation in the cases without and with corruption control. In the absence of corruption control, altruistic punishers are incapable of punishing corrupt punishers. Corrupt punishment maintains civilian cooperation but undermines the evolution of altruistic punishment. Otherwise, altruistic punishers can enforce symmetrical or asymmetrical punishment on both corrupt punishers and civilian defectors. In this case, both civilian cooperation and altruistic punishment can be promoted. And as an instrument of corruption control, the policy of asymmetrical punishment is more effective in fostering public cooperation and improving social welfare than symmetrical punishment. Moreover, no matter whether corruption control is considered or not, spiteful corruption that non-cooperative punishers penalize defectors is a more effective form for enhancing cooperation compared with bribery. Our work may thus offer an insight into the effects of corruption on public cooperation and the policy of anti-corruption.
惩罚被广泛认为是维持甚至增强公众合作的潜在促进因素，但同时也引发了二阶搭便车者的问题。特别是，最近的证据表明，如果惩罚者可以腐败，那么昂贵的惩罚就可以维持。然而，如何减少或消除腐败事件一直是人类社会的持久难题。由于权力不对称与等级制度有关，我们研究了在没有和有腐败控制的情况下，昂贵的惩罚如何影响合作的演变。在没有腐败控制的情况下，利他主义的惩罚者无法惩罚腐败的惩罚者。腐败的惩罚维持了平民的合作，但破坏了利他主义惩罚的进化。否则，利他主义的惩罚者可以对腐败的惩罚者和平民的叛徒实施对称或非对称的惩罚。在这种情况下，平民的合作和利他主义的惩罚都可以得到促进。作为腐败控制的一种手段，非对称惩罚政策在促进公共合作和提高社会福利方面比对称惩罚政策更有效。此外，无论是否考虑腐败控制，不合作的惩罚者对叛徒进行恶意腐败的惩罚形式比贿赂更能有效地增强合作。因此，我们的工作可以为理解腐败对公众合作和反腐败政策的影响提供一个视角。
