A Bilevel Consensus Model Based on Network Game for Maximizing Satisfaction and Minimizing Cost

Abstract

During the consensus reaching process (CRP), decision makers (DMs) typically achieve the desired consensus through discussion and persuasion. In this process, the moderator invests time and resources to persuade the DMs to change their opinions. Consequently, various interaction behaviors occur during the CRP, encompassing interactions between the moderator and DMs, as well as interactions among DMs. This article aims to develop a minimum cost-based consensus model by considering these interaction behaviors during the CRP. We utilize a network game to model the interplay among the behaviors of DMs and employ the Stackelberg game architecture to design an interactive mechanism between the DMs and the moderator. In the proposed model, the moderator provides compensation strategies and feedback suggestions to guide the DMs toward achieving the desired consensus level with minimal consensus cost. Meanwhile, the DMs adjust their opinions with the aim of maximizing their satisfaction. We then present an equilibrium analysis for the proposed model. Finally, we conduct an example application to illustrate and justify the performance of the proposed model.