Related papers: An Introduction to Mean Field Games using probabil…
We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…
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…
We construct Nash-equilibria in mean-field portfolio games of optimal investment and hedging under relative performance concerns with exponential (CARA) utility preferences. Common noise dynamics are modeled by integer-valued random…
The standard solution concept for stochastic games is Markov perfect equilibrium (MPE); however, its computation becomes intractable as the number of players increases. Instead, we consider mean field equilibrium (MFE) that has been…
We introduce the topic of learning in multiagent systems. We first provide a quick introduction to the field of game theory, focusing on the equilibrium concepts of iterated dominance, and Nash equilibrium. We show some of the most relevant…
In this paper we study a mean field model for discrete time, finite number of states, dynamic games. These models arise in situations that involve a very large number of agents moving from state to state according to certain optimality…
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…
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…
Agents attempt to maximize expected profits earned by selling multiple units of a perishable product where their revenue streams are affected by the prices they quote as well as the distribution of other prices quoted in the market by other…
In this paper, we study the infinite-time mean field games with discounting, establishing an equilibrium where individual optimal strategies collectively regenerate the mean-field distribution. To solve this problem, we partition all agents…
We formulate a mean field game where each player stops a privately observed Brownian motion with absorption. Players are ranked according to their level of stopping and rewarded as a function of their relative rank. There is a unique mean…
We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity,…
This paper studies singular mean field control problems and singular mean field stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some…
A novel framework is presented that combines Mean Field Game (MFG) theory and Hybrid Optimal Control (HOC) theory to obtain a unique $\epsilon$-Nash equilibrium for a non-cooperative game with switching and stopping times. We consider the…
We consider a deterministic mean field games problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect…
We formulate and solve a multi-player stochastic differential game between financial agents who seek to cost-efficiently liquidate their position in a risky asset in the presence of jointly aggregated transient price impact, along with…
The theory of Mean-Field Games is interested in the behaviour of interacting particle systems in which the individual interaction between particles (players) decreases as the size of the population increases. In recent years, it was…
Competitive games involving thousands or even millions of players are prevalent in real-world contexts, such as transportation, communications, and computer networks. However, learning in these large-scale multi-agent environments presents…
In this paper, we consider a mean field game model inspired by crowd motion in which several interacting populations evolving in $\mathbb R^d$ aim at reaching given target sets in minimal time. The movement of each agent is described by a…
Mean field games (MFG) and mean field control problems (MFC) are frameworks to study Nash equilibria or social optima in games with a continuum of agents. These problems can be used to approximate competitive or cooperative games with a…