A matrix approach to status quo analysis in the graph model for conflict resolution

An algebraic method is developed to carry out status quo analysis within the framework of the graph model for conflict resolution. As a form of post-stability analysis, status quo analysis aims at confirming that possible equilibria, or states stable for all decision-makers, are in fact reachable from the status quo or any other initial state. Although pseudo-codes for status quo analysis have been developed, they have never been implemented within a practical decision support system. The novel matrix approach to status quo analysis designed here is convenient for computer implementation and easy to employ, as is illustrated by an application to a real-world conflict case. Moveover, the proposed explicit matrix approach reveals an inherent link between status quo analysis and the traditional stability analysis and, hence, provides the possibility of establishing an integrated paradigm for stability and status quo analyses.