相关论文: Hilbert Space-Valued LQ Mean Field Games: An Infin…

This paper establishes a primal-dual formulation for continuous-time mean field games (MFGs) and provides a complete analytical characterization of the set of all Nash equilibria (NEs). We first show that for any given mean field flow, the…

In this paper, we consider discrete-time partially observed mean-field games with the risk-sensitive optimality criterion. We introduce risk-sensitivity behaviour for each agent via an exponential utility function. In the game model, each…

This paper is concerned with an overlapping information linear-quadratic (LQ) Stackelberg stochastic differential game with two leaders and two followers, where the diffusion terms of the state equation contain both the control and state…

In this paper, we introduce a framework of new mathematical representation of Game Theory, including static classical game and static quantum game. The idea is to find a set of base vectors in every single-player strategy space and to…

In this paper, we use mean field games (MFGs) to investigate approximations of $N$-player games with uniformly symmetrically continuous heterogeneous closed-loop actions. To incorporate agents' risk aversion (beyond the classical expected…

Multi-agent reinforcement learning, despite its popularity and empirical success, faces significant scalability challenges in large-population dynamic games. Graphon mean field games (GMFGs) offer a principled framework for approximating…

Mean-field games (MFGs) are a modeling framework for systems with a large number of interacting agents. They have applications in economics, finance, and game theory. Normalizing flows (NFs) are a family of deep generative models that…

In this paper, zero-sum mean-field type games (ZSMFTG) with linear dynamics and quadratic cost are studied under infinite-horizon discounted utility function. ZSMFTG are a class of games in which two decision makers whose utilities sum to…

We consider a class of linear-quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex…

This paper is devoted to the study of the long time behavior of Nash equilibria in Mean Field Games within the framework of displacement monotonicity. We first show that any two equilibria defined on the time horizon $[0,T]$ must be close…

Mean field games (MFG) and mean field control (MFC) problems have been introduced to study large populations of strategic players. They correspond respectively to non-cooperative or cooperative scenarios, where the aim is to find the Nash…

Competitive games involving thousands or even millions of players are prevalent in real-world contexts, such as transportation, communications, and computer networks. However, learning in these large-scale multi-agent environments presents…

We consider deterministic Mean Field Games (MFG) in all Euclidean space with a cost functional continuous with respect to the distribution of the agents and attaining its minima in a compact set. We first show that the static MFG with such…

This paper studies infinite horizon linear quadratic (LQ) mean field problems with common noise and regime switching, covering both control and game formulations. To establish a theoretical foundation for the LQ framework, we first analyze…

Independent learners are agents that employ single-agent algorithms in multi-agent systems, intentionally ignoring the effect of other strategic agents. This paper studies mean-field games from a decentralized learning perspective, with two…

This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop Nash equilibria are introduced. Existence of an open-loop Nash equilibrium…

In this paper, zero-sum mean-field type games (ZSMFTG) with linear dynamics and quadratic utility are studied under infinite-horizon discounted utility function. ZSMFTG are a class of games in which two decision makers whose utilities sum…

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 consider stochastic differential games with $N$ nearly identical players, linear-Gaussian dynamics, and infinite horizon discounted quadratic cost. Admissible controls are feedbacks for which the system is ergodic. We first study the…

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…