7. Stability Definitions: Hybrid Preference

In order to handle simultaneously simple preference, unknown preference and degrees of preference strength within the paradigm of the Graph Model for Conflict Resolution (GMCR), this chapter combines the structures described in the previous three chapters into what is called hybrid preference. Logical and matrix representations of Nash stability, general metarationality (GMR), symmetric metarationality (SMR) and sequential stability (SEQ) are developed for conflicts with hybrid preference. Detailed definitions are provided for three degrees of preference and any number of decision makers (DMs), which is sufficient to handle most conflicts arising in practice. The analysis of a conflict over proposed bulk exports of freshwater from the province of Newfoundland and Labrador, Canada, demonstrates how to determine stability results for graph models including unknown preferences as well as three degrees of preference. Readers of this chapter may wish to refer to Chaps. 4–6 for basic definitions of simple preference, unknown preference, and degrees of preference, respectively.