A Study of Consensus Formation using Kinetic Theory

In this paper consensus formation in multi-agent systems is studied using the framework of kinetic theory of gases. This can be done by interpreting agents as the molecules of a gas and interactions among agents as the collisions among the molecules. Each agent can interact with any other agent in the considered system and interactions are binary, i.e., they involve only two agents at a time. Under such hypothesis, starting from a microscopic model which describes the effects of interactions in a pair of agents, we derive, analytically, global properties of the system, such as the conservation of the average opinion. Simulation results show that the proposed kinetic approach allows reaching consensus and the velocity of convergence to consensus depends, as expected, on the parameters of the model.