Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games

By P. J. Graber, Alain Bensoussan. 2015

49 citations recorded by the source corpus.

We study a system of partial differential equations used to describe Bertrand and Cournot competition among a continuum of producers of an exhaustible resource. By deriving new a priori estimates, we prove the existence of classical solutions under general assumptions on the data. Moreover, under an additional hypothesis we prove uniqueness.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fb6e0d76b5a5e139ef4c091333db4e44ef6d8e12

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. Luciano Campi
2. Markus Fischer
3. P. J. Graber
4. Daniel Lacker

In Finance

1. Luciano Campi
2. Markus Fischer
3. P. J. Graber
4. Daniel Lacker
5. François Delarue

In Statistics and Probability

1. Luciano Campi
2. Markus Fischer
3. P. J. Graber
4. Daniel Lacker

Citations in the corpus

• $N$-player games and mean-field games with absorption (2016, background): “A rigorous study addressing existence and uniqueness issues in Chan and Sircar’s model has been subsequently done by [21].”
• Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource (2016, background): “) A well-posedness result for a related system of partial differential equations appears in a paper by Bensoussan and the present author [31].”