Coalition analysis with preference uncertainty in group decision support

Coalition analysis is extended to incorporate uncertain preference into three stability concepts, general metarationality (GMR), symmetric metarationality (SMR), and sequential stability (SEQ) under the paradigm of the graph model for conflict resolution. As a follow-up analysis in the graph model, coalition analysis aims to assess whether equilibriums under individual calculations are vulnerable to coalition moves and countermoves and, hence, become unstable under coalition stabilities. Coalition analysis has been considered for transitive graph models with simple preference under four stabilities, Nash, GMR, SMR, and SEQ, as well as general graph models with uncertain preference for the Nash stability. This paper introduces preference uncertainty into coalition stabilities under GMR, SMR, and SEQ for general graph models that can be transitive or intransitive. Depending on the focal coalition's different attitudes towards preference uncertainty, four different extensions are presented. Interrelationships of coalition stabilities are investigated within each extension and across the four extensions. A case study is carried out to illustrate how to apply the proposed coalition stabilities.