Strength of preference in the graph model for conflict resolution

A new preference structure that includes a simple relative measure of strength of preference is developed and integrated into some of the stability definitions for the graph model for conflict resolution. In this triplet preference structure, a decision-maker may greatly prefer or prefer one state or scenario to another, or may be indifferent between them. Four stability definitions ( solution concepts), Nash stability ( R), general metarationality ( GMR), symmetric metarationality ( SMR), and sequential stability ( SEQ), are extended to include strong and weak stabilities for the case of conflicts with two decision makers. Theorems that clarify the interrelationships of the strong and weak versions of these solution concepts are presented. The application of this new preference structure and the associated solution concepts is demonstrated in an environmental conflict model, called the Sustainable Development Conflict. This case shows that valuable strategic insights are gained when strength of preference is integrated into the stability analysis.