Multi-agent systems with multiple-wise interaction: Propagation of chaos and macroscopic limit

Abstract: We consider interacting multi-agent systems where the interaction is not only pairwise but involves simultaneous interactions among multiple agents (multiple-wise interaction). By passing through the mesoscopic and macroscopic limits with a fixed multiple-wise interaction of order $m$, we derive a macroscopic equation in the limit $m \rightarrow \infty$, capturing the dominant effects in large-size multiple-wise order.