Related papers: Linear-Quadratic Mean Field Games in Hilbert space…
We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this…
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…
In this paper, we focus on stationary (ergodic) mean-field games (MFGs). These games arise in the study of the long-time behavior of finite-horizon MFGs. Motivated by a prior scheme for Hamilton-Jacobi equations introduced in Aubry-Mather's…
Motivated by a product pricing problem, a linear-quadratic Stackelberg differential game for a regime switching system involving one leader and two followers is studied. The two followers engage in a zero-sum differential game, and both the…
In the first part of this paper, we derive an infinite dimensional partial differential equation which describes an economic equilibrium in a model of storage which includes an infinite number of non-atomic agents. This equation has the…
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…
This paper studies uniform stabilization and social optimality for linear quadratic (LQ) mean field control problems with multiplicative noise, where agents are coupled via dynamics and individual costs. The state and control weights in…
We exploit the structure of geometric graphs on Riemannian manifolds to analyze strategic dynamic graphs at the limit, when the number of nodes tends to infinity. This framework allows to preserve intrinsic geometrical information about the…
We consider a class of non-cooperative N-player non-zero-sum stochastic differential games with singular controls, in which each player can affect a linear stochastic differential equation in order to minimize a cost functional which is…
While the general theory for the terminal-initial value problem in mean-field games is widely used in many models of applied mathematics, the modeling potential of the corresponding forward-forward version is still under-considered. In this…
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…
We establish the convergence of the deep actor-critic reinforcement learning algorithm presented in [Angiuli et al., 2023a] in the setting of continuous state and action spaces with an infinite discrete-time horizon. This algorithm provides…
The paper is concerned with a zero-sum Stackelberg stochastic linear-quadratic (LQ, for short) differential game over finite horizons. Under a fairly weak condition, the Stackelberg equilibrium is explicitly obtained by first solving a…
In Mean Field Games of Controls, the dynamics of the single agent is influenced not only by the distribution of the agents, as in the classical theory, but also by the distribution of their optimal strategies. In this paper, we study…
We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games…
We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized…
In the paper, we use the equivalent formulation of a finite state mean field game as a control problem with mixed constraints to study the dependence of solutions to finite state mean field game on an initial distribution of players. We…
Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they often fail to capture critical non-linearities inherent in…
In this paper, we consider a linear quadratic stochastic two-person zero-sum differential game. The controls for both players are allowed to appear in both drift and diffusion of the state equation. The weighting matrices in the performance…
In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. The state space of a generic agent is a compact Borel space. At every time, each agent is randomly…