Multiple levels of preference in interactive strategic decisions

A multiple-level preference ranking structure is developed within the paradigm of the Graph Model for Conflict Resolution to study multi-objective decision making in conflict situations more realistically. In this structure, a decision maker may have multiple levels of preference for one state or scenario over another; for example, if state A is preferred to state B, it may be mildly preferred at level 1, more strongly preferred at level 2, ……, or maximally preferred at level rr, where r>0r>0 is a fixed parameter. The number of levels, rr, is unrestricted in this system, thereby extending earlier two-level (r=1r=1) and three-level (r=2r=2) structures. Multilevel versions of four stability definitions, Nash stability, general metarationality, symmetric metarationality, and sequential stability, are defined for the graph model with this extended preference structure, and the relationships among them are investigated. A specific case study, including multiple decision makers and multiple levels of preference, is carried out to illustrate how the new solution concepts can be applied in practice.