Selfish-dilemma consensus analysis for group decision making in the perspective of cooperative game theory

In group decision making, an adjustment mechanism is activated when individual decision information is evidently discrepant. This situation requires some decision makers (DMs) to revise their original judgments. This paper assumes that DMs are selfish, so none of them willingly adjust their initial judgments, and each always hopes any required adjustment will be as minimal. However, the egoism of the DMs may lead to the failure to reach a consensus. To cope with this issue, a fair and reasonable consensus adjustment mechanism is fundamental, one which can counteract the selfishness of DMs and promote consensus-reaching. To do this, we build a model to identify the minimum consensus adjustment of each DM, which relates to the root of the selfish dilemma. Then, we introduce the concept of selfish-dilemma consensus adjustment cooperative games, whose coalition payoffs are defined as the consensus adjustments that they have to undertake to avoid the selfish-dilemma. Furthermore, two payoff indices, the Shapley value and the nucleolus, are introduced for the minimum total consensus adjustment allocation, ensuring the DMs’ adjustments are as fair and reasonable as possible. Finally, a numerical example is offered, and a comparative analysis is made. This method is the first to focus on Pareto-optimal consensus adjustment allocation in a fair and efficient way.