Matrix representation of conflicts with two decision-makers

New matrix representations are developed for characterizing potential human interactions under conflict within the structure of the graph model for conflict resolution for the case of a dispute having two decision makers. The matrix representations are devised for calculating individual stability and equilibria for strategic interactions defined according to the solution concepts consisting of Nash stability, general meta- rationality, symmetric metarationality, and sequential stability. A potential military confrontation is utilized to illustrate the procedures for applying the matrix representation of solution concepts to a practical problem. Compared with the existing systems, matrix representation of solution concepts for graph models is more effective and convenient for calculating stabilities and predicting equilibria, especially in complex conflict models with many feasible states. Moreover, the method is easy to code and can be extended to other contexts such as those that allow preference uncertainty.