7 research outputs found
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 work
we demonstrate that the closed-loop Nash equilibrium derived in the
infinite-population limit through approaches (i) and (iv) are identical
Large Banks and Systemic Risk: Insights from a Mean-Field Game Model
This paper aims to investigate the impact of large banks on the financial
system stability. To achieve this, we employ a linear-quadratic-Gaussian (LQG)
mean-field game (MFG) model of an interbank market, which involves one large
bank and multiple small banks. Our approach involves utilizing the MFG
methodology to derive the optimal trading strategies for each bank, resulting
in an equilibrium for the market. Subsequently, we conduct Monte Carlo
simulations to explore the role played by the large bank in systemic risk under
various scenarios. Our findings indicate that while the major bank, if its size
is not too large, can contribute positively to stability, it also has the
potential to generate negative spillover effects in the event of default,
leading to increased systemic risk. We also discover that as banks become more
reliant on the interbank market, the overall system becomes more stable but the
probability of a rare systemic failure increases. This risk is further
amplified by the presence of a large bank, its size, and the speed of interbank
trading. Overall, the results of this study provide important insights into the
management of systemic risk
LQG Risk-Sensitive Mean Field Games with a Major Agent: A Variational Approach
Risk sensitivity plays an important role in the study of finance and
economics as risk-neutral models cannot capture and justify all economic
behaviors observed in reality. Risk-sensitive mean field game theory was
developed recently for systems where there exists a large number of
indistinguishable, asymptotically negligible and heterogeneous risk-sensitive
players, who are coupled via the empirical distribution of state across
population. In this work, we extend the theory of Linear Quadratic Gaussian
risk-sensitive mean-field games to the setup where there exists one major agent
as well as a large number of minor agents. The major agent has a significant
impact on each minor agent and its impact does not collapse with the increase
in the number of minor agents. Each agent is subject to linear dynamics with an
exponential-of-integral quadratic cost functional. Moreover, all agents
interact via the average state of minor agents (so-called empirical mean field)
and the major agent's state. We develop a variational analysis approach to
derive the best response strategies of agents in the limiting case where the
number of agents goes to infinity. We establish that the set of obtained
best-response strategies yields a Nash equilibrium in the limiting case and an
-Nash equilibrium in the finite player case. We conclude the paper
with an illustrative example