An Alternative Approach to Mean Field Game with Major and Minor Players, and Applications to Herders Impacts

Rene A. Carmona, Peiqi Wang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The goal of the paper is to introduce a formulation of the mean field game with major and minor players as a fixed point on a space of controls. This approach emphasizes naturally the role played by McKean–Vlasov dynamics in some of the players’ optimization problems. We apply this approach to linear quadratic models for which we recover the existing solutions for open loop equilibria, and we show that we can also provide solutions for closed loop versions of the game. Finally, we implement numerically our theoretical results on a simple model of flocking.

Original languageEnglish (US)
Pages (from-to)5-27
Number of pages23
JournalApplied Mathematics and Optimization
Volume76
Issue number1
DOIs
StatePublished - Aug 1 2017

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

Fingerprint Dive into the research topics of 'An Alternative Approach to Mean Field Game with Major and Minor Players, and Applications to Herders Impacts'. Together they form a unique fingerprint.

Cite this