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.

中文翻译：

---

探索在逆图模型框架内实现所需解决方案的最低成本冲突中介路径


现有的冲突解决逆图模型 （GMCR） 研究主要集中在识别决策者 （DM） 所需的偏好，以便期望状态是平衡的。然而，没有探讨从当前状态过渡到所需平衡的过程。在本文中，我们提出了一个考虑偏好调整成本的最小调整成本模型，以确定所需状态成为均衡所需的偏好。随后，我们首次引入了过渡成本的概念，以量化指导 DM 从一种状态过渡到另一种状态所涉及的费用，并开发了一个最低成本冲突调解路径模型。该模型旨在确定最有效的路径，以最大限度地降低从当前状态过渡到所需平衡的成本。此外，为了适应对多个期望均衡的考虑，我们扩展了最低成本冲突调解路径模型，以分析和确定从当前状态过渡到具有总体最低成本的已确定期望均衡之一的最佳路径。此外，为了解决过渡成本的不确定性，我们制定了一个概率最大化冲突调解路径模型，该模型考虑了调解过程可用的有限预算。最后，利用现实世界的争议，即加拿大新不伦瑞克省的压裂冲突来演示所提出的模型的应用。