Related papers: Quadratic Mean Field Games
In a probabilistic mean field game driven by a L\'evy process an individual player aims to minimize a long run discounted/ergodic cost by controlling the process through a pair of increasing and decreasing c\`adl\`ag processes, while he is…
Linear-quadratic Gaussian games provide a framework for modeling strategic interactions in multi-agent systems, where agents must estimate system states from noisy observations while also making decisions to optimize a quadratic cost.…
We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and…
Financial markets and more generally macro-economic models involve a large number of individuals interacting through variables such as prices resulting from the aggregate behavior of all the agents. Mean field games have been introduced to…
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…
Quantum games represent the really 21st century branch of game theory, tightly linked to the modern development of quantum computing and quantum technologies. The main accent in these developments so far was made on stationary or repeated…
We consider a class of $N$-player games and mean-field games of singular controls with ergodic performance criterion, providing a benchmark case for irreversible investment games featuring mean-field interaction and strategic…
This paper focuses on linear-quadratic (LQ for short) mean-field games described by forward-backward stochastic differential equations (FBSDEs for short), in which the individual control region is postulated to be convex. The decentralized…
In this paper we study a type of games regularized by the relative entropy, where the players' strategies are coupled through a random environment variable. Besides the existence and the uniqueness of equilibria of such games, we prove that…
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…
In this paper, we investigate the existence and uniqueness of solutions to a stationary mean field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian with possibly singular congestion effects.…
Mean-field theory has been extensively explored in decision analysis of {large-scale} (LS) systems but traditionally in ``pure" cooperative or competitive settings. This leads to the so-called mean-field game (MG) or mean-field team (MT).…
This paper considers a linear-quadratic (LQ) mean field control problem involving a major player and a large number of minor players, where the dynamics and costs depend on random parameters. The objective is to optimize a social cost as a…
Conventional Mean-field games/control study the behavior of a large number of rational agents moving in the Euclidean spaces. In this work, we explore the mean-field games on Riemannian manifolds. We formulate the mean-field game Nash…
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been…
We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…
This article studies linear-quadratic Stackelberg games between two dominating players (or equivalently, leaders) and a large group of followers, each of whom interacts under a mean field game (MFG) framework. Unlike the conventional…
In [14], Gueant, Lasry and Lions considered the model problem ``What time does meeting start?'' as a prototype for a general class of optimization problems with a continuum of players, called Mean Field Games problems. In this paper we…
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the…
Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics…