Optimizing the cost of preference manipulation in the graph model for conflict resolution

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.