Determining state space anomalies in mean field games

TL;DR

This paper addresses the inverse problem of identifying anomalies in the state space of stationary mean field games, providing new theoretical results on their unique identifiability across various practical scenarios.

Contribution

It introduces the first analysis of state space anomalies in nonlinear coupled MFG systems, establishing novel uniqueness results for their structure and parameters.

Findings

Proves unique identifiability of anomalies in MFG systems

Applies results to traffic flow, economics, and epidemics

First to analyze anomalies in nonlinear coupled MFGs

Abstract

In this paper, we are concerned with the inverse problem of determining anomalies in the state space associated with the stationary mean field game (MFG) system. We establish novel unique identifiability results for the intrinsic structure of these anomalies in mean field games systems, including their topological structure and parameter configurations, in several general scenarios of practical interest, including traffic flow, market economics and epidemics. To the best of our knowledge, this is the first work that considers anomalies in the state space for the nonlinear coupled MFG system.