Set-Driven Evolution for Multiagent System

We consider the deterministic evolution in the Euclidean space of a multiagent system with a large number of agents (possibly infinitely many). At each instant of time, besides from time and its current position, the set of velocities available to each agent is influenced by the set described by the current position of all the other agents. The latter is in turn determined by the overall motion of the crowd of all the agents. The interplay to the microscopical point of view of each single agent, and the macroscopical one of the set-evolution yields a non-trivial dynamical system. This two-level multiagent system can be described either by the evolution of a probability measure-describing the instantaneous density of the crowd-or by the evolution of a set-describing the positions where there is at least one agent. In this paper, we precise the links between the two descriptions, providing also some quantitative estimates on the macroscopical admissible evolutions.