5. Stability Definitions: Unknown Preference

To account for uncertainty in the preferences of a decision maker (DM), the simple preference framework put forward in Chap. 4 is expanded to handle unknown preference, in which a DM simply does not know the preference relationship of one or more pairs of states. The strategic impacts of unknown preferences can be ascertained by employing variations of the earlier stability definitions. As presented in this chapter, Nash, general metarational, symmetric metarational and sequential stability can determine stable states for each DM, as well as the equilibria or potential resolutions, even when some preferences are unknown. They are defined for conflicts with two, or more than two, DMs, for both the logical and matrix representations of the Graph Model for Conflict Resolution (GMCR). A sustainable development dispute and a conflict over the bulk export of water illustrate how the versatile techniques put forward in this chapter can be used to ascertain rigorously the strategic effects of unknown preference. Readers interested in unknown preferences should also refer to the foundational material on simple preference in Chap. 4, as well as Chaps. 6 and 7, which describe approaches to address other preference structures.