Bidirectional supervision: An effective method to suppress corruption and defection under the third party punishment mechanism of donation games

Corruption is a serious problem faced by human society, which significantly affects the efficiency of the third party punishment mechanism. Without intervention, fair umpires will gradually evolve into bribed umpires to maximize its own profits, resulting in a double dilemma of corruption-defection. Therefore, it is worth studying how to suppress corruption through effective intervention mechanisms. In this paper, we propose a bidirectional supervision mechanism in which players could also supervise umpires and give up the games if they find their corresponding umpires are unfavourable for themselves. Five parameters control the whole model. Through Monte Carlo simulations, we reveal the effects of these parameters on the results. More importantly, the bidirectional supervision mechanism has a significant effect on suppressing corruption and defection. Our results provide a new perspective for exploring how corruption and defection could be suppressed under the third-party punishment mechanism.