Preference strength and uncertainty in the graph model for conflict resolution for two decision-makers

A new preference structure that includes preference strength and preference uncertainty is developed within the paradigm of the graph model for conflict resolution with two decision makers. This structure allows a decision maker to strongly or mildly prefer one state or scenario over another, to have equal preference for the two states, or to be uncertain about the preference between them, thereby creating a more general preference structure. Four solution concepts, Nash Stability, General Metarationality, Symmetric Metarationality, and Sequential Stability, are defined for the graph model with this extended preference structure, and relationships among stability types are determined. A specific graph model with two decision makers is used to illustrate how the new solution concepts can be applied in practice.