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Using the observed or desired stability results of each decision maker (DM) and the equilibrium of a conflict, an algorithm is proposed that determines whether the Nash, general metarationality, symmetric metarationality or sequential stability definition best explains the observations or how to achieve the desired equilibrium. The matrix representation of the graph model for conflict resolution, normally used to determine stabilities that reflect different models of human interaction in conflict, is utilized here to keep track of available one-step moves for each DM, as well as the DMs’ relative preferences among states. A key theorem involving matrix representation of graph models determines which stability types are consistent with the observations or achievement of the desired equilibrium, taking into account specified preferences of the DMs, for the case of two or more DMs. To illustrate the use of the algorithm in practice, behavioral analysis is applied to a softwood lumber dispute between Canada and the USA. [ABSTRACT FROM AUTHOR]