Related papers: Graphon Mean Field Games with a Representative Pla…
This paper considers mean field games with optimal stopping time (OSMFGs) where agents make optimal exit decisions, the coupled obstacle and Fokker-Planck equations in such models pose challenges versus classic MFGs. This paper proposes a…
In this article, we introduce a new class of entropy-penalized robust mean field game problems in which the representative agent is opposed to Nature. The agent's objective is formulated as a min-max stochastic control problem, in which…
In this paper, we consider a finite horizon, non-stationary, mean field games (MFG) with a large population of homogeneous players, sequentially making strategic decisions, where each player is affected by other players through an aggregate…
We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…
We consider a multi-agent Markov strategic interaction over an infinite horizon where agents can be of multiple types. We model the strategic interaction as a mean-field game in the asymptotic limit when the number of agents of each type…
We investigate mean-field games (MFG) in which agents can actively control their speed of access to information. Specifically, the agents can dynamically decide to obtain observations with reduced delay by accepting higher observation…
In this paper, we study a class of discrete-time mean-field games under the infinite-horizon risk-sensitive discounted-cost optimality criterion. Risk-sensitivity is introduced for each agent (player) via an exponential utility function. In…
We apply the generalized conditional gradient algorithm to potential mean field games and we show its well-posedeness. It turns out that this method can be interpreted as a learning method called fictitious play. More precisely, each step…
This paper establishes an equilibrium existence result for a class of Mean Field Games involving Reflected Stochastic Differential Equations. The proof relies on the framework of relaxed controls and martingale problems.
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 establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company…
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.…
We find closed-form solutions to the stochastic game between a broker and a mean-field of informed traders. In the finite player game, the informed traders observe a common signal and a private signal. The broker, on the other hand,…
The emergence of the graphon theory of large networks and their infinite limits has enabled the formulation of a theory of the centralized control of dynamical systems distributed on asymptotically infinite networks (Gao and Caines, IEEE…
We present a new approach to solving games with a countably or uncountably infinite number of players. Such games are often used to model multiagent systems with a large number of agents. The latter are frequently encountered in economics,…
Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malham\'e, Mean…
This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an…
In this paper, we present a model of a game among teams. Each team consists of a homogeneous population of agents. Agents within a team are cooperative while the teams compete with other teams. The dynamics and the costs are coupled through…
Mean field games (MFGs) are a promising framework for modeling the behavior of large-population systems. However, solving MFGs can be challenging due to the coupling of forward population evolution and backward agent dynamics. Typically,…
We consider learning approximate Nash equilibria for discrete-time mean-field games with nonlinear stochastic state dynamics subject to both average and discounted costs. To this end, we introduce a mean-field equilibrium (MFE) operator,…