Abstract Conflicts occur when different parties have different evaluations regarding the resolution of some issue and each one of them can change the conflict scenario in more than one way. These conflicts may occur at various levels from the personal scale to conflicts involving large blocks of countries and various types of conflict costs might be involved, such as: economic, social and environmental. In many situations, offering incentives to alter the preferences of some decision makers (DMs) might be an effective way to achieve desirable stable scenarios. The Graph Model for Conflict Resolution (GMCR) is a model that has long been used to model and analyze conflicts because it is flexible and easy to calibrate. The purpose of this paper is to present ideas on how to work with the inverse GMCR to optimize costs in changing the preferences of each DM to achieve desired equilibrium states within the conflict. We propose some methods to aggregate costs of changing DMs’ preferences. The purpose is to determine the lowest aggregate cost of preference changes that makes a given desired state an equilibrium according to a given stability notion. Besides formally describing the problem, we study some properties of the minimum costs for different stability notions and show that the computational complexity of the optimal preference manipulation problem is NP-hard. We apply this method to analyze the Cuban missile conflict.

中文翻译：

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优化图模型中偏好操作的成本以解决冲突

摘要 当各方对某个问题的解决方案有不同的评价，并且每一方都可以以不止一种方式改变冲突情景时，就会发生冲突。这些冲突可能发生在各个层面，从个人规模到涉及大块国家的冲突，可能涉及各种类型的冲突成本，例如：经济、社会和环境。在许多情况下，提供激励来改变某些决策者 (DM) 的偏好可能是实现理想的稳定情景的有效方法。冲突解决图模型 (GMCR) 是一种长期以来用于对冲突进行建模和分析的模型，因为它灵活且易于校准。本文的目的是提出有关如何使用逆 GMCR 来优化改变每个 DM 偏好的成本的想法，以在冲突中实现所需的平衡状态。我们提出了一些方法来汇总改变 DM 偏好的成本。目的是确定偏好变化的最低总成本，使给定的期望状态根据给定的稳定性概念达到平衡。除了正式描述问题外，我们还研究了不同稳定性概念的最小成本的一些性质，并表明最优偏好操作问题的计算复杂度是 NP 难的。我们应用这种方法来分析古巴导弹冲突。目的是确定偏好变化的最低总成本，使给定的期望状态根据给定的稳定性概念达到平衡。除了正式描述问题外，我们还研究了不同稳定性概念的最小成本的一些性质，并表明最优偏好操作问题的计算复杂度是 NP 难的。我们应用这种方法来分析古巴导弹冲突。目的是确定偏好变化的最低总成本，使给定的期望状态根据给定的稳定性概念达到平衡。除了正式描述问题外，我们还研究了不同稳定性概念的最小成本的一些性质，并表明最优偏好操作问题的计算复杂度是 NP 难的。我们应用这种方法来分析古巴导弹冲突。