Toward a Kinetic Framework to Model the Collective Dynamics of Multi-agent Systems

Abstract

The investigation of the collective dynamics of multi-agent systems in terms of the study of the properties of single agents is not feasible when the number of interacting agents is large. In this case, the collective dynamics can be better examined by adopting a statistical approach that studies the long-time asymptotic properties of the system as a whole. The kinetic framework discussed in this paper can be used to study collective and emergent properties of large and decentralized multi-agent systems once single interactions among agents are properly described. Moreover, the discussed framework can be used to design how agents should interact to ensure that the resulting multi-agent system would exhibit the required collective and emergent characteristics. The discussed framework restricts the interactions among agents to message exchanges, and it assumes that the investigated properties emerge from interactions. As an example of the use of the framework, and to outline a concrete application of it, the properties of a system in which agents implement the symmetric gossip algorithm are analyzed. Analytic results obtained using the discussed framework are compared with independent simulations, showing the effectiveness of the approach.