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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 …