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 ef-ficiency 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 corrup-tion 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 pa-rameters control the whole model. Through Monte Carlo simulations, we reveal the effects of these parameters on the results. More importantly, the bidirectional supervision mech-anism 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.(c) 2023 Elsevier Inc. All rights reserved.