A kinetic approach to investigate the collective dynamics of multi-agent systems

When the number of interacting agents in a multi-agent system is large, the detailed study of the dynamics of each agent tends to obfuscate the collective and possibly emergent dynamics of the multi-agent system as a whole. When the interest is on the collective properties of the multi-agent system, a statistical study of the dynamics of the states of the agents can provide a more effective perspective on the system. In particular, a statistical approach can better focus on the long-term asymptotic properties of the studied multi-agent system. The initial part of this paper outlines a framework to approach the study of the collective properties of multi-agent systems. The framework targets large and decentralized multi-agent systems in which the relevant collective properties emerge from interactions. Then, the paper exemplifies the use of the framework to study the long-term asymptotic properties of multi-agent systems in which agents interact using the symmetric gossip algorithm. The state of each agent is represented as a real number, and the use of the framework shows that all agents exponentially converge to the average of their initial states. The analytic results provided by the framework are confirmed by independent multi-agent simulations. Finally, the paper is concluded with a brief discussion of related work and an overview of future extensions.