相关论文: Graphon Mean Field Games and the GMFG Equations

The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game…

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 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 is concerned with a new class of mean-field games which involve a finite number of agents. Necessary and sufficient conditions are obtained for the existence of the decentralized open-loop Nash equilibrium in terms of…

This paper studies stochastic games on large graphs and their graphon limits. We propose a new formulation of graphon games based on a single typical player's label-state distribution. In contrast, other recently proposed models of graphon…

In this paper, we study a model of network formation in large populations. Each agent can choose the strength of interaction (i.e. connection) with other agents to find a Nash equilibrium. Different from the recently-developed theory of…

In many real-world large-scale decision problems, self-interested agents have individual dynamics and optimize their own long-term payoffs. Important examples include the competitive access to shared resources (e.g., roads, energy, or…

We study Nash equilibria for a sequence of symmetric $N$-player stochastic games of finite-fuel capacity expansion with singular controls and their mean-field game (MFG) counterpart. We construct a solution of the MFG via a simple iterative…

Mean-field games (MFG) have become significant tools for solving large-scale multi-agent reinforcement learning problems under symmetry. However, the assumption of exact symmetry limits the applicability of MFGs, as real-world scenarios…

The Mean-Field approximation is a tractable approach for studying large population dynamics. However, its assumption on homogeneity and universal connections among all agents limits its applicability in many real-world scenarios.…

We design and analyze reinforcement learning algorithms for Graphon Mean-Field Games (GMFGs). In contrast to previous works that require the precise values of the graphons, we aim to learn the Nash Equilibrium (NE) of the regularized GMFGs…

We analyze a system of partial differential equations that model a potential mean field game of controls, briefly MFGC. Such a game describes the interaction of infinitely many negligible players competing to optimize a personal value…

We consider the problem of representing collective behavior of large populations and predicting the evolution of a population distribution over a discrete state space. A discrete time mean field game (MFG) is motivated as an interpretable…

This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations…

In this paper, we study graphon mean field games using a system of forward-backward stochastic differential equations. We establish the existence and uniqueness of solutions under two different assumptions and prove the stability with…

This paper is concerned with an indefinite linear-quadratic mean field games of stochastic large-population system, where the individual diffusion coefficients can depend on both the state and the control of the agents. Moreover, the…

We consider network aggregative games to model and study multi-agent populations in which each rational agent is influenced by the aggregate behavior of its neighbors, as specified by an underlying network. Specifically, we examine systems…

Pressure on ancillary reserves, i.e.frequency preserving, in power systems has significantly mounted due to the recent generalized increase of the fraction of (highly fluctuating) wind and solar energy sources in grid generation mixes. The…

Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players…

We propose an approach to modelling large-scale multi-agent dynamical systems allowing interactions among more than just pairs of agents using the theory of mean field games and the notion of hypergraphons, which are obtained as limits of…