Proceedings of the 2009 IEEE International Conference on Systems, Man, and Cybernetics San Antonio, TX, USA - October 2009 Interrelationships among Attitude-Based and Conventional Stability Concepts within the Graph Model for Conflict Resolution Takehiro Inohara Keith W. Hipel Department of Value and Decision Science Department of Systems Design Engineering Tokyo Institute of Technology, Tokyo, Japan University of Waterloo, Waterloo, Ontario, Canada
[email protected] [email protected] Abstract—Propositions are presented on interrelationships in [18]. The concept of policies, which is similar to that of among attitude-based and conventional stability concepts within strategies in game theory [28], is introduced to the graph the paradigm of Graph Model for Conflict Resolution. In fact, model framework in [36], [37]. Research on the topic of the authors verify the following properties: if decision makers’ attitudes are discrete and decision makers’ preferences are incomplete preference information is also carried out [25], complete and anti-symmetric, then i) relational Nash stability is [29]. Cooperative decision situations are also analyzed within equivalent to Nash stability, ii) relational general metarationality GMCR [34]. is equivalent to general metarationality, iii) relational symmetric In a conflict, the attitudes of the various DMs can signifi- metarationality is equivalent to symmetric metarationality, and iv) relational sequential stability is equivalent to sequential cantly influence the outcome of the conflict. Thus, analyzing stability; under totally neutral attitudes of decision makers, i) the conflict as well as the accompanying attitudes is useful for relational Nash stability is equivalent to relational symmetric better understanding a given conflict. Attitude-based analysis metarationality, and ii) relational general metarationality is allows decision analysts to examine a lot of potential conflicts equivalent to relational sequential stability.