Toward Practical Forecasts of Public Sentiments via Convexification for Mean Field Games: Evidence from Real World COVID-19 Discussion Data

TL;DR

This paper demonstrates a convexification-based numerical method for forecasting public sentiment dynamics using Mean Field Games, validated with real COVID-19 social media data, showing promising alignment with observed sentiment patterns.

Contribution

It provides the first proof-of-concept that MFG models can effectively capture complex public sentiment evolution from real-world data.

Findings

Sentiment density predictions closely match observed data.

Convexification guarantees global convergence to the MFG solution.

Framework lays groundwork for systematic parameter identification.

Abstract

We apply a convexification-based numerical method to forecast public sentiment dynamics using Mean Field Games (MFGs). The theoretical foundation for the convexification approach, established in our prior work, guarantees global convergence to the unique solution to the MFG system. The present work demonstrates the practical potential of this framework using real-world sentiment data extracted from social media public discussion during the COVID-19 pandemic. The results show that the MFG model with appropriate parameters and convexification yields sentiment density predictions that align closely with observed data and satisfy the governing equations. While current parameter selection relies on manual calibration, our findings establish the first proof-of-concept evidence that MFG models can capture complex temporal patterns in public sentiment, laying the groundwork for future work on systematic parameter identification methods, i.e. solutions of coefficient inverse problems for the MFG system.