A kinetic model of the dynamics of compromise in large multi-agent systems

Compromise is one of the primary phenomena that govern the dynamics of the opinion in multi-agent systems. In this paper, compromise is isolated from other phenomena, and it is studied using a statistical framework designed to investigate collective properties of large multi-agent systems. The proposed framework is completed with the details needed to model compromise, and differential problems which describe the dynamics of the opinion under suitable hypotheses are presented. Long-time asymptotic solutions of obtained differential problems are discussed to confirm that compromise makes multi-agent systems tend to reach consensus. It is proved that compromise makes all agents tend to share the same opinion, and that the value of the asymptotic opinion can be expressed in terms of the characteristics of the multi-agent system and of the initial distribution of the opinion. Obtained analytic results are confirmed by independent simulations in an illustrative case.