# Conservation laws arising in the study of forward-forward Mean-Field Games

## TL;DR

This paper explores the connection between forward-forward Mean Field Game models and hyperbolic conservation laws, analyzing their mathematical properties and long-term behavior to advance understanding of stationary MFGs.

## Contribution

It establishes a novel link between forward-forward MFGs and hyperbolic conservation laws, and studies existence and long-time dynamics of solutions.

## Key findings

- Link established between forward-forward MFGs and hyperbolic conservation laws
- Existence of solutions for the models proven
- Long-time behavior of solutions analyzed

## Abstract

We consider forward-forward Mean Field Game (MFG) models that arise in numerical approximations of stationary MFGs. First, we establish a link between these models and a class of hyperbolic conservation laws as well as certain nonlinear wave equations. Second, we investigate existence and long-time behavior of solutions for such models.