6. Stability Definitions: Degrees of Preference

Two nations sharing an oil field spanning their common border may greatly prefer a peaceful division of the benefits to warfare, but may be at an impasse because each is uncertain how seriously the other takes the issue. The objective of this chapter is to expand the concept of simple preference to address situations in which the strength, level or degree of preference is important. To account for the strategic consequences of degree of preference, the definitions of Nash stability, general metarationality (GMR), symmetric metarationality (SMR) and sequential stability (SEQ) must be extended. Logical representations of Nash, GMR, SMR and SEQ are determined for conflicts in which two decision makers (DMs), or more than two, may have any degree of preference. Matrix representations of these four stability definitions are formulated for up to three degrees of preference for any number of DMs. An international environmental conflict is utilized to demonstrate how four degrees of preference can affect strategy choices and outcomes of a dispute. Foundational material on simple preference is furnished in Chap. 4, while other preference structures are described in Chaps. 5 and 7.