For many group decision-making (GDM) issues, such as water-resource allocation, urban resettlement, and traffic-route planning, the benefits of the decision makers (DMs) are closely related to the collective decision-making result. In fact, the consensus-reaching process is a game between the decision makers and the moderator. The fairness concern in GDM impacts DMs’ preference modification and influences consensus achievement, but it has long been ignored because most studies have focused on the consensus mechanism or cost. We introduced the fairness concern into the consensus-reaching process in GDM and established an equilibrium mechanism for GDM. Specifically, we proposed a general consensus game that considers the decision fairness concern. Then, we proved the existence of the Nash Equilibrium between the decision makers and the moderator and established a consensus model with a minimum compensation cost. A simulated annealing algorithm was designed to solve for an equilibrium solution. Through numerical examples used in previous studies and an application example of green supply chain management, we analyzed the relationship between fairness concern, the degree of coordination, and effectiveness in GDM and demonstrated the impact of the fairness concern on consensus achievement.

对于许多群体决策（GDM）问题，例如水资源分配，城市移民安置和交通路线规划，决策者（DM）的利益与集体决策的结果紧密相关。实际上，达成共识的过程是决策者和主持人之间的博弈。GDM中的公平性影响会影响DM的偏好修改并影响共识达成，但由于大多数研究都集中在共识机制或成本上，因此长期以来一直被忽略。我们在GDM达成共识的过程中引入了对公平的关注，并建立了GDM的均衡机制。具体来说，我们提出了一种考虑决策公平性的通用共识博弈。然后，我们证明了决策者和主持人之间存在纳什均衡，并建立了具有最小补偿成本的共识模型。设计了模拟退火算法来求解平衡解。通过先前研究中使用的数值示例和绿色供应链管理的应用示例，我们分析了公平关注，协调程度和GDM有效性之间的关系，并证明了公平关注对达成共识的影响。