相关论文: LQG Mean Field Games with a Major Agent: Nash Cert…

The partially observed major minor LQG and nonlinear mean field game (PO MM LQG MFG) systems where it is assumed the major agent's state is partially observed by each minor agent, and the major agent completely observes its own state have…

This paper delves into studying the differences and connections between open-loop and closed-loop strategies for the linear quadratic (LQ) mean field games (MFGs) by the direct approach. The investigation begins with the finite-population…

We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chain by means of semimartingale and the weak formulation of stochastic optimal control, our…

We develop a variational approach to address risk-sensitive optimal control problems with an exponential-of-integral cost functional in a general linear-quadratic-Gaussian (LQG) single-agent setup, offering new insights into such problems.…

Mean field games with a major player were introduced in (Huang, 2010) within a linear-quadratic (LQ) modeling framework. Due to the rich structure of major-minor player models, the past ten years have seen significant research efforts for…

Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…

This paper studies a large population dynamic game involving nonlinear stochastic dynamical systems with agents of the following mixed types: (i) a major agent, and (ii) a population of $N$ minor agents where $N$ is very large. The major…

We develop a convex analysis approach for solving LQG optimal control problems and apply it to major-minor (MM) LQG mean-field game (MFG) systems. The approach retrieves the best response strategies for the major agent and all minor agents…

We study discrete-time mean-field Markov games with infinite numbers of agents where each agent aims to minimize its ergodic cost. We consider the setting where the agents have identical linear state transitions and quadratic cost…

In this paper, we consider a mean field game (MFG) with a major and $N$ minor agents. We first consider the limiting problem and allow the coefficients to vary with the conditional distribution in a nonlinear way. We use the stochastic…

This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…

This paper continues the study of the mean field game (MFG) convergence problem: In what sense do the Nash equilibria of $n$-player stochastic differential games converge to the mean field game as $n\rightarrow\infty$? Previous work on this…

We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…

We consider a controlled linear-quadratic (LQ) large-population system with mixture of three types agents: major leader, minor leaders and minor followers. The Stackelberg-Nash-Cournot (SNC) approximate equilibrium is studied by a…

Mean field games (MFGs) model equilibria in games with a continuum of weakly interacting players as limiting systems of symmetric $n$-player games. We consider the finite-state, infinite-horizon problem with ergodic cost. Assuming Markovian…

In the context of large population symmetric games, approximate Nash equilibria are introduced through equilibrium solutions of the corresponding mean field game in the sense that the individual gain from optimal unilateral deviation under…

We develop a probabilistic framework to approximate Nash equilibria in symmetric $N$-player games in the large population regime, via the analysis of associated mean field games (MFGs). The approximation is achieved through the analysis of…

In the presence of a common noise, we study the convergence problems in mean field game (MFG) and mean field control (MFC) problem where the cost function and the state dynamics depend upon the joint conditional distribution of the…

This paper investigates a class of mixed stochastic linear-quadratic-Gaussian (LQG) social optimization and Nash game in the context of a large scale system. Two types of interactive agents are involved: a major agent and a large number of…

We study a general class of entropy-regularized multi-variate LQG mean field games (MFGs) in continuous time with $K$ distinct sub-population of agents. We extend the notion of actions to action distributions (exploratory actions), and…