School of Mathematical Sciences, Beihang University, Beijing 100191, China.
Department of Mathematics and Computer Science, Hengshui University, Hengshui 053000, China.
Chaos. 2022 Jun;32(6):063138. doi: 10.1063/5.0088493.
Public goods games are widely used to model social dilemmas involving multiple agents. Though defection is the only rational choice for an individual in a public goods game, cooperative behavior is observed in a variety of social dilemmas, which is the subject of our research. Punishing defectors has been shown to be an effective mechanism for promoting cooperation, but it relies on the third-party umpire being fair. In this article, an umpire intervention model with corruption is proposed to explore the impact of corruption on punishment mechanisms. In our model, players and umpires operate in a multilayer network. The players play public goods games, which are overseen by umpires. Fair umpires punish defectors, whereas corrupt umpires take bribes from defectors rather than meting out a punishment. We separately explore the effects of the fraction of fair umpires , the spatial distribution, and the fine cost α and bribe cost β. Our Monte Carlo simulation shows that the above factors have a significant impact on cooperation. Intervention by an umpire always improves social efficiency, even for an entirely corrupt system. Moreover, relatively developed systems can resist corruption. Staggered and centralized distributions always have opposite effects on cooperative behavior, and these effects depend on and r. We also find that whether cooperators fully occupy the player layer depends only on whether β reaches a certain threshold.
公共物品博弈广泛用于模拟涉及多个主体的社会困境。尽管在公共物品博弈中，个体的背叛是唯一理性的选择，但在各种社会困境中都观察到了合作行为，这是我们研究的主题。惩罚背叛者已被证明是促进合作的有效机制，但它依赖于第三方裁判的公正。在本文中，提出了一种具有腐败的裁判干预模型，以探讨腐败对惩罚机制的影响。在我们的模型中，玩家和裁判在多层网络中运作。玩家进行公共物品博弈，由裁判监督。公正的裁判会惩罚背叛者，而腐败的裁判则会收受贿赂而不是给予惩罚。我们分别探讨了公正裁判的比例、空间分布以及罚款成本 α 和贿赂成本 β 的影响。我们的蒙特卡罗模拟表明，上述因素对合作有显著影响。裁判的干预总是会提高社会效率，即使对于完全腐败的系统也是如此。此外，相对发达的系统可以抵抗腐败。交错和集中分布对合作行为总是有相反的影响，这些影响取决于和 r。我们还发现，合作者是否完全占据玩家层仅取决于 β 是否达到某个阈值。
