Fuzzy Preferences in the Graph Model for Conflict Resolution

Abstract

A new framework for the graph model for conflict resolution is developed so that decision makers (DMs) with fuzzy preferences can be included in conflict models. A graph model is both a formal representation for multiple participant-multiple objective decision problems and a set of analysis procedures that add insights into them. Within the new framework, graph models can include-and integrate into the analysis-both certain and uncertain information about DMs' preferences. One key contribution of this study is to extend the four basic stability definitions for two or more DMs to models with fuzzy preferences. Together, fuzzy Nash stability, fuzzy general metarationality, fuzzy symmetric metarationality, and fuzzy sequential stability provide anuanced description of human behavior. A state is fuzzy stable for a DM if a move to any other state is not sufficiently likely to yield an outcome which the DM prefers, where sufficiency is measured according to a fuzzy satisficing threshold that is the characteristic of the DM. A fuzzy equilibrium, which is an outcome that is fuzzy stable for all DMs, therefore represents a possible resolution of the strategic conflict. The practical application and interpretation of these new stability definitions are illustrated with an example.