The graph model for composite decision makers and its application to a water resource conflict

Abstract

To analyze a strategic conflict involving composite decision makers (CDMs), this paper uses the methodology of the Graph Model for Conflict Resolution (GMCR). A CDM is a group of individuals with differing decision characteristics – conservative or aggressive – any one of whom can make a decision on behalf of the group. In our model, a conservative CDM makes moves that take into account the interests of all group members, aiming to protect each one from possible sanctions; an aggressive CDM gives priority to some individuals that will benefit and does not necessarily consider the interests of other group members when making moves. Based on these different decision characteristics, two versions of hesitant fuzzy stability definitions, indexed I and II, are proposed. To facilitate the stability analysis of the graph model with multiple decision makers (DMs), including at least one CDM, a matrix-based method called Matrix Representation for Hesitant Fuzzy Stability is developed to identify the equilibria of the model, or states that are stable for all DMs and are therefore possible resolutions of the conflict. A water resource conflict in the Lancang-Mekong River basin is utilized to demonstrate the system. The results reveal how the decision characteristics of CDMs can influence the equilibria of a conflict.