Steering the distribution of agents in mean-field and cooperative games

TL;DR

This paper develops a method to steer large populations of weakly interacting agents towards a desired distribution using mean-field and cooperative game frameworks, extending optimal mass transport theory.

Contribution

It introduces a novel approach linking terminal costs to target distributions, expanding the application of optimal mass transport in agent distribution control.

Findings

The map from terminal costs to distributions is onto.

Extension of optimal mass transport theory to agent distribution steering.

Framework applicable to mean-field and cooperative game settings.

Abstract

The purpose of this work is to pose and solve the problem to guide a collection of weakly interacting dynamical systems (agents, particles, etc.) to a specified terminal distribution. The framework is that of mean-field and of cooperative games. A terminal cost is used to accomplish the task; we establish that the map between terminal costs and terminal probability distributions is onto. Our approach relies on and extends the theory of optimal mass transport and its generalizations.