Forward-Forward Mean Field Games in mathematical modeling with application to opinion formation and voting models

TL;DR

This paper explores the forward-forward mean field games framework, demonstrating its well-posedness and applicability to modeling opinion formation and social dynamics where agents adapt based on past information.

Contribution

It introduces the forward-forward mean field games approach, analyzing its mathematical properties and showing its relevance to social modeling scenarios.

Findings

Proved well-posedness of the forward-forward mean field game system.

Demonstrated applicability to opinion formation models.

Provided insights into social dynamics modeling.

Abstract

While the general theory for the terminal-initial value problem in mean-field games is widely used in many models of applied mathematics, the modeling potential of the corresponding forward-forward version is still under-considered. In this work, we study the well-posedness of the problem in a quite general setting and explain how it is appropriate to model a system of players that have a complete knowledge of the past states of the system and are adapting to new information without any knowledge about the future. Then we show how forward-forward mean field games can be effectively used in mathematical models for opinion formation and other social phenomena.