LQG Mean Field Games with a Major Agent: Nash Certainty Equivalence versus Probabilistic Approach

Mean field game systems consisting of a major agent and a large population of minor agents were introduced in (Huang, 2010) in an LQG setup. In the past years several approaches towards major-minor mean field games have been developed, principally (i) the Nash certainty equivalence (Huang, 2010), (ii) master equations, (iii) asymptotic solvability, and (iv) the probabilistic approach. In a recent work (Huang, 2020), for the LQG case the equivalence of the solutions obtained via approaches (i)-(iii) was established. In this talk we first review approaches (i) and (iv). We then demonstrate that the closed-loop Nash equilibrium derived in the infinite-population limit through (i) and (iv) are identical.

Biography:

Dena Firoozi is an Assistant Professor in the Department of Decision Sciences at HEC Montr茅al (business school of University of Montreal). Before joining HEC Montr茅al, she was a postdoctoral fellow in the mathematical finance program of the Department of Statistical Sciences at the University of Toronto, Canada, between 2018-2020. She was also a PhD exchange student in the same program during Fall 2017. She received her Ph.D. degree in electrical engineering, systems & control specialization, from 黑料不打烊 University, Canada, in 2019. Dena's research interests are in mean field games, stochastic control, estimation theory, and their applications in financial and energy markets.