相关论文: Optimal stopping in mean field games, an obstacle …

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 are interested in the study of stochastic games for which each player faces an optimal stopping problem. In our setting, the players may interact through the criterion to optimise as well as through their dynamics. After briefly…

We present a new notion of solution for mean field games master equations. This notion allows us to work with solutions which are merely continuous. We prove first results of uniqueness and stability for such solutions. It turns out that…

We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it as $n\to\infty$. However, both the finite and…

A game-theoretic framework for time-inconsistent stopping problems where the time-inconsistency is due to the consideration of a non-linear function of an expected reward is developed. A class of mixed strategy stopping times that allows…

This paper revisits the well-studied \emph{optimal stopping} problem but within the \emph{large-population} framework. In particular, two classes of optimal stopping problems are formulated by taking into account the \emph{relative…

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…

In this article we study the convergence of the Nash Equilibria in a N-player differential game towards the optimal strategies in the Mean Field Games, when the dynamic of the generic player includes a reflection process which guarantees…

We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…

We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to…

Mean field games are limit models for symmetric $N$-player games with interaction of mean field type as $N\to\infty$. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate…

We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become…

We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…

Standard Markovian optimal stopping problems are consistent in the sense that the first entrance time into the stopping set is optimal for each initial state of the process. Clearly, the usual concept of optimality cannot in a…

We study an infinite-horizon discrete-time optimal stopping problem under non-exponential discounting. A new method, which we call the iterative approach, is developed to find subgame perfect Nash equilibria. When the discount function…

When modeling robot interactions as Nash equilibrium problems, it is desirable to place coupled constraints which restrict these interactions to be safe and acceptable (for instance, to avoid collisions). Such games are continuous with…

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…

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 first study an optimal stopping problem in which a player (an agent) uses a discrete stopping time in order to stop optimally a payoff process whose risk is evaluated by a (non-linear) $g$-expectation. We then consider a non-zero-sum…

First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results…