An Analytic Model of the Impact of Skeptical Agents on the Dynamics of Compromise

This paper studies analytically the dynamics of the opinion in multi-agent systems where two classes of agents coexist. The fact that the population of considered multi-agent systems is divided into two classes is meant to account for agents with different propensity to change their opinions. Skeptical agents, which are agents that are not inclined to change their opinions, can be modeled together with moderate agents, which are agents that are moderately open to take into account the opinions of the others. The studied analytic model of opinion dynamics involves only compromise, which describes how agents change their opinions to try to reach consensus. The adopted model of compromise is stochastic in order to give agents some level of autonomy in their decisions. Presented results show, analytically, that after a sufficient number of interactions consensus is reached, regardless of the initial distribution of the opinion. Analytic results are confirmed by simulations shown in the last part of the paper.