MEAN FIELD GAMES: A TOY MODEL ON AN ERDOS-RENYI GRAPH

By François Delarue. 2017

50 citations recorded by the source corpus.

The purpose of this short article is to address a simple example of a game with a large number of players in mean field interaction when the graph connection between them is not complete but is of the Erdos-Renyi type. We study the quenched convergence of the equilibria towards the solution of a mean field game. To do so, we follow recent works on the convergence problem for mean field games and we heavily use the fact that the master equation of the asymptotic game has a strong solution.

Subfields: Condensed Matter Physics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/30845f056298e3335f36195147cdcec8acbace4d

How researchers see this paper

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

In Condensed Matter Physics

1. Alexander Aurell
2. Mathieu Laurière
3. René A. Carmona
4. Daniel Lacker

In Finance

1. Daniel Lacker
2. René A. Carmona
3. Mathieu Laurière
4. Alexander Aurell
5. Markus Fischer
6. François Delarue
7. Franccois Delarue
8. Pierre Cardaliaguet

In Mathematical Physics

1. Daniel Lacker
2. Alexander Aurell
3. Mathieu Laurière
4. René A. Carmona

Citations in the corpus

• Stochastic Graphon Games: II. The Linear-Quadratic Case (2021, methodology): “In the dynamic setting, [11] considers a MFG with an Erdös–Renyi graph replacing the standard MFG interaction (a complete graph with uniform weights).”
• On the convergence of closed-loop Nash equilibria to the mean field game limit (2018, background): “The idea of using the master equation to prove limit theorems has proven to be powerful and quite versatile, subsequently adapted to to models with finite state space [2, 21], local interactions [9], interactions governed by random graphs [23], and models with a major player [10].”