We consider open multi-agent systems, which are systems subject to frequent arrivals and departures of agents while the studied process takes place. We study the behavior of all-to-all pairwise gossip interactions in such open systems. Arrivals and departures of agents imply that the composition and size of the system evolve with time, and in particular prevent convergence. We describe the expected behavior of the system by showing that the evolution of scale-independent quantities can be characterized exactly by fixed-size linear dynamical systems that correspond to Markov processes with states of potentially unbounded dimension. For this purpose we develop a general methodology that could be applicable to larger classes of models. We apply this approach to characterize the evolution of the two first moments (and thus also of a variance-like measure of disagreement) for open systems of fixed and variable size.

翻译：暂无翻译