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

TL;DR

This paper studies multi-agent systems with complex multi-wise interactions, deriving macroscopic equations as the interaction order grows large, revealing dominant effects in large systems.

Contribution

It introduces a framework for analyzing multi-agent systems with multiple-wise interactions and derives macroscopic limits as the interaction order increases.

Findings

Derived macroscopic equations from multi-wise interaction models.

Analyzed the limit behavior as interaction order tends to infinity.

Provided insights into the dominant effects in large multi-agent systems.

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.