Evolution of cooperation in a hierarchical society with corruption control

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.