An inverse graph model for conflict resolution under opinion dynamics with minimum cost

Abstract

Existing inverse graph model for conflict resolution (GMCR) primarily focuses on identifying opinions that can make the desired state an equilibrium, while overlooking the opinion dynamics among conflicting members and the transition costs involved in shifting from the current opinions to those that establish the desired equilibrium state. Accordingly, this study proposes an inverse GMCR with minimum cost in the framework of the social network DeGroot (SNDG) model. Recognizing the pivotal influence of leaders’ initial opinions and self-confidence levels on the formation of consensus under the SNDG model, this study introduces two inverse graph models. The first model aims to minimize the adjustment of leaders’ initial opinions, while the second seeks to minimize changes in their self-confidence levels. Both models incorporate bounded confidence constraints, capturing the limited extent to which leaders are willing to modify their initial opinions or self-confidence levels. Additionally, the models are designed to allow conflicting members to adopt conflict behaviors that best align with their individual circumstances. Finally, the practical application of the proposed method is demonstrated through the Elmira groundwater contamination conflict, accompanied by sensitivity and comparative analysis to validate its effectiveness and superiority.