Mean Field Games with a Dominating Player

By Alain Bensoussan, Michael Chau, Phillip S. C. Yam. 2014

95 citations recorded by the source corpus.

In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the dominating player. We first provide the general theory and discuss the necessary condition for the optimal controls and equilibrium condition by adopting adjoint equation approach. We then present a special case in the context of linear-quadratic framework, in which a necessary and sufficient condition can be asserted by stochastic maximum principle; we finally establish the sufficient condition that guarantees the unique existence of the equilibrium control. The proof of the convergence result of finite player game to mean field counterpart is provided in Appendix.

Subfields: Economics and Econometrics, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/4d8217123ded2faa1bc70f0ac08793c61d462a75

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. Pierre Cardaliaguet
2. Xiuneng Zhu
3. Alessio Porretta
4. Marco Cirant
5. René A. Carmona
6. Daniel Lacker
7. Markus Fischer
8. François Delarue

In Finance

1. Alessio Porretta
2. Pierre Cardaliaguet
3. Peiqi Wang
4. Marco Cirant
5. Xiuneng Zhu
6. René A. Carmona
7. Daniel Lacker
8. Diogo A. Gomes

In Modeling and Simulation

1. Peiqi Wang
2. René A. Carmona
3. Alessio Porretta
4. Pierre Cardaliaguet
5. Xiuneng Zhu

Citations in the corpus

• An Alternative Approach to Mean Field Game with Major and Minor Players, and Applications to Herders Impacts (2016, background): “As a result, the finite-player game which is actually solved in [1], is merely a N -player game including only the minor players.”
• Splitting methods and short time existence for the master equations in mean field games (2020, background): “Mean field games with a major player have been first discussed by Huang in [20] and several notions of equilibria, in different contexts, have been proposed in the literature since then: see [5, 6, 7, 8, 11, 13, 14, 15, 26].”
• A Probabilistic Approach to Mean Field Games with Major and Minor Players (2014, methodology): “In [3], the authors take, like in [25], a stochastic Hamilton-Jacobi-Bellman approach to a type of general mean field games with major and minor players, and the limiting problem is characterized by a set of stochastic PDEs.”