Consensus Analysis for Large-Scale Group Decision Making Based on Two-Stage Nash-Bargaining Game

Due to the characteristic differences of decision makers (DMs), such as growth experience, educational background, social status, and personal beliefs, individual decision information often varies. It becomes more prominent in large-scale group decision making (LSGDM). Therefore, consensus discussion is necessary to make the final decision result represent all DMs' opinions as much as possible. In this regard, this article analyzes the conflicts between individual and subgroup adjustments and between subgroup and group adjustments by the built models. Concerning intrasubgroup adjustment surplus and intersubgroup adjustment surplus, we regard them as cost allocation problems in cooperative games under the consensus constraint. Then, the two-stage Nash-bargaining consensus adjustment game (NBCAG) is introduced to make the allocation result as fair as possible. Meanwhile, the Nash-bargaining consensus adjustment scheme for LSGDM is proposed. Considering the heterogeneity of DMs and subgroups, two-stage asymmetrical NBCAGs are further constructed. In light of these results, a new LSGDM method is proposed. Numerical and comparative analysis is also performed. This article offers the first LSGDM method that emphasizes the fairness and Pareto optimality of consensus adjustment by two-stage Nash-bargaining games.