Matrix representations of the inverse problem in the graph model for conflict resolution

Given the final individual stability for each decision maker or an equilibrium of interest, a matrix-based method for an inverse analysis is developed in order to calculate all of the possible preferences for each decision maker creating the stability results based on the Nash, general metarationality, symmetric metarationality, or sequential stability definition of possible human interactions in a conflict. The matrix representations are furnished for the relative preferences, unilateral movements and improvements, as well as joint movements and joint improvements for a conflict having two or more decision makers. Theoretical conditions are derived for specifying required preference relationships in an inverse graph model. Under each of the four solution concepts, a matrix relationship is established to obtain all the available preferences for each decision maker causing the specific state to be an equilibrium. To explain how it can be employed in practice, this new approach to inverse analysis is applied to the Elsipogtog First Nation fracking dispute which took place in the Canadian Province of New Brunswick.