# Stationary Discounted and Ergodic Mean Field Games of Singular Control

arXiv: https://arxiv.org/abs/2105.07213 · HTML: https://mlsanity.com/paper/2105.07213/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2021.

## Built on by (most cited first, 1 of 1)

- [Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations](https://mlsanity.com/paper/2202.06637/) (2022)

## Abstract (arXiv)

We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games finds natural applications in the context of optimal productivity expansion in dynamic oligopolies. We prove existence and uniqueness of the mean field equilibria, which are completely characterized through nonlinear equations. Furthermore, we relate the mean field equilibria for the discounted and the ergodic games by showing the validity of an Abelian limit. The latter allows also to approximate Nash equilibria of - so far unexplored - symmetric N-player ergodic singular control games through the mean field equilibrium of the discounted game. Numerical examples finally illustrate in a case study the dependency of the mean field equilibria with respect to the parameters of the games.