Stability Definitions: Simple Preference

Abstract

Stability definitions describing a range of human behavior under conflict are presented for decision makers (DMs) having simple preferences in order to establish the concepts of stable states and equilibria in both the logical and matrix formulations of the Graph Model for Conflict Resolution (GMCR). For a DM with simple preference, a state or scenario is either more, less or equally preferred to another state in a conflict model. A state is stable for a DM if all of the DM’s available unilateral improvements can be blocked by specified patterns of countermoves by the other (sanctioning) DMs. The logical interpretation of GMCR, and the idea of interactive moves, are the basis of the four stability definitions presented in this chapter: Nash stability, general metarationality (GMR), symmetric metarationality (SMR) and sequential stability (SEQ). The logical definitions can be converted to equivalent matrix representations, which improve the computational performance of the engine of the decision support system described in Chap. 10. The contents of Chap. 3 provide background modeling for the definitions for this chapter, which in turn constitutes the launching pad for the preference structures built up in Chaps. 5, 6 and 7.