Exploring the minimum cost conflict mediation path to a desired resolution within the inverse graph model framework

The existing inverse graph model for conflict resolution (GMCR) research primarily concentrates on identifying the required preferences of decisions makers (DMs) such that a desired state is an equilibrium. However, the process of transitioning from the current state to the desired equilibrium is not explored. In this paper, we propose a minimum adjustment cost model taking account of preference adjustment costs to identify the required preferences for a desired state to be an equilibrium. Subsequently, we introduce the concept of transition costs for the first time to quantify expenses involved in guiding a DM transition from one state to another and develop a minimum cost conflict mediation path model. This model aims to identify the most efficient path that minimizes the cost of transitioning from the current state to the desired equilibrium. Moreover, to accommodate the consideration of multiple desired equilibria, we extend the minimum cost conflict mediation path model to analyze and determine the optimal path for transitioning from the current state to one of the identified desired equilibria with the overall minimum cost. Furthermore, to address uncertainty surrounding transition costs, we formulate a probability maximizing conflict mediation path model that considers a limited budget available for the mediation process. Finally, a real-world dispute, the fracking conflict in the province of New Brunswick, Canada, is utilized to demonstrate the application of the proposed models.