The influence of externality in the graph model for conflict resolution under fuzzy preferences

The Graph Model for Conflict Resolution (GMCR) is a flexible and comprehensive methodology for systematically investigating strategic conflicts. However, most existing studies solely focus on internal conflicts among decision makers (DMs), often disregarding the influence of external stakeholders (ESs) on DMs' preferences. Consequently, this leads to insufficient stability in equilibrium outcomes. The objective of this study is to address the conflict issue faced by DMs with subjective uncertain preferences who are influenced by externality. Building upon the framework of GMCR, this study proposes the graph model for conflict resolution with fuzzy preference based on externality (FEGMCR) which introduces fuzzy numbers to measure both uncertain preferences of DMs and uncertain expectations of ESs. Furthermore, four forms of stability are extended- Fuzzy Nash Stability based on externality (FER), Fuzzy General Metarationality based on externality (FEGMR), Fuzzy Symmetric Metarationality based on externality (FESMR), and Fuzzy Sequential Stability based on externality (FESEQ). The optimal equilibrium is achieved by dynamically adjusting the weight of the impact of externalities. Finally, the method is applied to the case of plastic ban in Hainan. It is found that the expectations of ESs do change the preferences of DMs and affect the final equilibrium, which provides a sustainable solution for the issue.