  Motivated by the development of dynamics in probability spaces, we propose a
novel multi-agent dynamic of consensus type where each agent is a probability
measure. The agents move instantaneously towards a weighted barycenter of the
ensemble according to the 2-Wasserstein metric. We mathematically describe the
evolution as a system of measure differential inclusions and show the existence
of solutions for compactly supported initial data. Inspired by the
consensus-based optimization, we apply the multi-agent system to solve a
minimization problem over the space of probability measures. In the small
numerical example, each agent is described by a particle approximation and aims
to approximate a target measure.
