相关论文: Game on Random Environment, Mean-field Langevin Sy…

We consider multi-player games played on graphs, in which the players aim at fulfilling their own (not necessarily antagonistic) objectives. In the spirit of evolutionary game theory, we suppose that the players have the right to repeatedly…

Mean field games (MFGs) have emerged as a powerful framework for modeling interactions in large-scale multi-agent systems. Despite recent advancements in reinforcement learning (RL) for MFGs, existing methods are typically limited to finite…

We consider an $N$-player game where the states of the players evolve with time as Stochastic Differential Equations (SDEs) with interaction only in the drift terms. Each player controls the drift of the SDE satisfied by her state process,…

Estimating the unknown reward functions driving agents' behaviors is of central interest in inverse reinforcement learning and game theory. To tackle this problem, we develop a unified framework for reward function recovery in two-player…

We obtain global, non-asymptotic convergence guarantees for independent learning algorithms in competitive reinforcement learning settings with two agents (i.e., zero-sum stochastic games). We consider an episodic setting where in each…

We address learning Nash equilibria in convex games under the payoff information setting. We consider the case in which the game pseudo-gradient is monotone but not necessarily strictly monotone. This relaxation of strict monotonicity…

The goal of the paper is to introduce a formulation of the mean field game with major and minor players as a fixed point on a space of controls. This approach emphasizes naturally the role played by McKean-Vlasov dynamics in some of the…

A central challenge in game theory and learning systems such as GANs is understanding which algorithms can efficiently compute equilibria across the heterogeneous landscape of games. Equilibrium computation is typically studied solver by…

Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…

We consider a symmetric $n$-player nonzero-sum stochastic differential game with controlled jumps and mean-field type interaction among the players. Each player minimizes some expected cost by affecting the drift as well as the jump part of…

Constrained Markov games offer a formal mathematical framework for modeling multi-agent reinforcement learning problems where the behavior of the agents is subject to constraints. In this work, we focus on the recently introduced class of…

A major challenge in multi-agent systems is that the system complexity grows dramatically with the number of agents as well as the size of their action spaces, which is typical in real world scenarios such as autonomous vehicles, robotic…

We investigate mean field game systems under invariance conditions for the state space, otherwise called {\it viability conditions} for the controlled dynamics. First we analyze separately the Hamilton-Jacobi and the Fokker-Planck…

Gradient flows play a substantial role in addressing many machine learning problems. We examine the convergence in continuous-time of a \textit{Fisher-Rao} (Mean-Field Birth-Death) gradient flow in the context of solving convex-concave…

We here address the question of restoration of uniqueness in mean-field games deriving from deterministic differential games with a large number of players. The general strategy for restoring uniqueness is inspired from earlier similar…

In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…

The theory of Mean Field Game of Controls considers a class of mean field games where the interaction is through the joint distribution of the state and control. It is well known that, for standard mean field games, certain monotonicity…

We consider a stationary Mean Field Games system defined on a network. In this framework, the transition conditions at the vertices play a crucial role: the ones here considered are based on the optimal control interpretation of the…

Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this…

The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…