Finite Mean Field Games: Fictitious play and convergence to a first order continuous mean field game

By Saeed Hadikhanloo, Francisco J. Silva. Journal des Mathématiques Pures et Appliquées, 2018

60 citations recorded by the source corpus.

In this article we consider finite Mean Field Games (MFGs), i.e. with finite time and finite states. We adopt the framework introduced in Gomes Mohr and Souza in 2010, and study two seemly unexplored subjects. In the first one, we analyze the convergence of the fictitious play learning procedure, inspired by the results in continuous MFGs. In the second one, we consider the relation of some finite MFGs and continuous first order MFGs. Namely, given a continuous first order MFG problem and a sequence of refined space/time grids, we construct a sequence finite MFGs whose solutions admit limits points and every such limit point solves the continuous first order MFG problem.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/31770cf7da730c69e753d5a0f200f6dd41b1539e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Zhuoran Yang
2. Kaiqing Zhang
3. Tamer Basar

In Finance

1. Zhuoran Yang
2. Kaiqing Zhang
3. Tamer Basar

In Management Science and Operations Research

1. Zhuoran Yang
2. Kaiqing Zhang
3. Tamer Basar
4. Jieyi Long
5. Ekram Hossain
6. Amal Feriani

Citations in the corpus

• Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms (2019, background): “Note that the aforementioned works focus on the settings with either finite horizon (Hadikhanloo and Silva, 2019; Elie et al., 2019) or stationary mean-field equilibria (Guo et al.”