相关论文: On non-uniqueness in mean field games

A basic question for zero-sum repeated games consists in determining whether the mean payoff per time unit is independent of the initial state. In the special case of "zero-player" games, i.e., of Markov chains equipped with additive…

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…

We introduce a simple class of mean field games with absorbing boundary over a finite time horizon. In the corresponding $N$-player games, the evolution of players' states is described by a system of weakly interacting It\^o equations with…

This work is mainly concerned with the so-called limit theory for mean-field games. Adopting the weak formulation paradigm put forward by Carmona and Lacker, we consider a fully non-Markovian setting allowing for drift control and…

The mean field games system is a coupled pair of nonlinear partial differential equations arising in differential game theory, as a limit as the number of agents tends to infinity. We prove existence and uniqueness of classical solutions…

We propose a new mean-field game model with two states to study synchronization phenomena, and we provide a comprehensive characterization of stationary and dynamic equilibria along with their stability properties. The game undergoes a…

In this paper we study the long time behaviour of mean field games systems with fractional diffusion, modeling the case that the individual dynamics of the players is driven by independent jump processes and controlled through the drift…

We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…

We consider stochastic differential games with a large number of players, with the aim of quantifying the gap between closed-loop, open-loop and distributed equilibria. We show that, under two different semi-monotonicity conditions, the…

Mean field games model equilibria in games with a continuum of players as limiting systems of symmetric $n$-player games with weak interaction between the players. We consider a finite-state, infinite-horizon problem with two cost criteria:…

Mean field games is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play non-cooperative dynamic games…

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…

An average-time game is played on the infinite graph of configurations of a finite timed automaton. The two players, Min and Max, construct an infinite run of the automaton by taking turns to perform a timed transition. Player Min wants to…

A general class of mean field games are considered where the governing dynamics are controlled diffusions in $\mathbb{R}^d$. The optimization criterion is the long time average of a running cost function. Under various sets of hypotheses,…

This paper studies the n-player game and the mean field game under the CRRA relative performance on terminal wealth, in which the interaction occurs by peer competition. In the model with n agents, the price dynamics of underlying risky…

We consider both $N$-player and mean-field games of optimal portfolio liquidation in which the players are not allowed to change the direction of trading. Players with an initially short position of stocks are only allowed to buy while…

Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics…

In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the…

In this short note, we consider an inverse problem to a mean-field games system where we are interested in reconstructing the state-independent running cost function from observed value-function data. We provide an elementary proof of a…

We explore a mechanism of decision-making in Mean Field Games with myopic players. At each instant, agents set a strategy which optimizes their expected future cost by assuming their environment as immutable. As the system evolves, the…