Interrelationships among attitude-based and conventional stability concepts within the graph model for conflict resolution

Propositions are presented on interrelationships among attitude-based and conventional stability concepts within the paradigm of graph model for conflict resolution. In fact, the authors verify the following properties: if decision makers´ attitudes are discrete and decision makers´ preferences are complete and anti-symmetric, then (i) relational Nash stability is equivalent to Nash stability, (ii) relational general metarationality is equivalent to general metarationality, (iii) relational symmetric metarationality is equivalent to symmetric metarationality, and (iv) relational sequential stability is equivalent to sequential stability; under totally neutral attitudes of decision makers, (i) relational Nash stability is equivalent to relational symmetric metarationality, and (ii) relational general metarationality is equivalent to relational sequential stability.