Two analytic models of compromise in multi-agent systems

This paper studies compromise, which is the tendency of agents to move their opinions towards those of agents they interact with, trying to reach consensus. Compromise is one of the most important phenomena in the study of opinion dynamics, and this paper presents two analytic models to study it. First, agents are considered deterministic and a preliminary model of the effects of compromise is derived. Then, the model is generalized to give agents some level of autonomy by modelling their behaviour in terms of a stochastic process. Both models are analytic and they can be used to study collective properties of multi-agent systems starting from the details of single interactions among agents. Analytic results concerning the conservation of the average opinion for both models are verified by simulation in the last part of the paper.