This paper introduces the Categorical Graph Model for Conflict Resolution (C-GMCR), a novel framework that integrates category theory into the traditional Graph Model for Conflict Resolution (GMCR). The C-GMCR framework provides a more abstract and general way to model and analyze conflict resolution, enabling researchers to uncover deeper insights and connections. We present the basic concepts, methods, and an application of the C-GMCR framework to the well-known Prisoner's Dilemma and other representative cases. The findings suggest that the categorical approach offers new perspectives on stability concepts and can potentially lead to the development of more effective conflict resolution strategies.
This study discusses the analysis method for obtaining solutions that allow de-escalation in international conflicts within the framework of the Graph Model for Conflict Resolution. CD games, a conflict type in which two decision-makers can choose Cooperate (C) or Defect (D) strategies, are analyzed by examining the state transition and stability of decision makers with a focus on reachability. Based on the analysis, a new conceptual set is proposed, called 'de-escalation reachability,' which enables focused analysis on the conflict states while avoiding any influence of arbitrators' attributes.
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