State transition time analysis in the Graph Model for Conflict Resolution

•New conflict analysis methodologies are developed.•The methodologies allow to deal with state transition time in a conflict.•New stability concepts are proposed and their interrelationships are examined.•The new methodologies are applied to a modified prisoners' dilemma situation.•The application demonstrates how the newly proposed methodologies work.

New conflict analysis methodologies which allow the analysts to deal with state transition time in a conflict are developed within the framework of the Graph Model for Conflict Resolution. The methodologies include new variety of stability concepts, whose interrelationships with the existent standard stability concepts are verified in the propositions in this paper. A modified version of the Prisoners' Dilemma situation is analyzed as a simple example of conflicts in order to demonstrate how the newly proposed methodologies work.