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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…
This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an…
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…
In this paper we discuss a class of mean field linear-quadratic-Gaussian (LQG) games for large population system which has never been addressed by existing literature. The features of our works are sketched as follows. First of all, our…
In this paper, we investigate a class of mean field games where the mean field interactions are achieved through the joint (conditional) distribution of the controlled state and the control process. The strategies are of $open\;loop$ type,…
We identify structural assumptions which provide solvability of the Nash system arising from a linear-quadratic closed-loop game, with stable properties with respect to the number of players. In a setting of interactions governed by a…
In this paper, we consider discrete-time partially observed mean-field games with the risk-sensitive optimality criterion. We introduce risk-sensitivity behaviour for each agent via an exponential utility function. In the game model, each…
In this paper, we study a class of linear-quadratic (LQ) mean field games of controls with common noises and their corresponding $N$-player games. The theory of mean field game of controls considers a class of mean field games where the…
The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…
This paper focuses on linear-quadratic (LQ for short) mean-field games described by forward-backward stochastic differential equations (FBSDEs for short), in which the individual control region is postulated to be convex. The decentralized…
We consider mean field games with ergodic cost in the framework of a general discrete time controlled Markov processes. The state space of the processes is given by a general $\sigma$-compact Polish space. Under certain conditions, we show…
In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a locally compact Polish…
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,…
We consider a general class of nonzero-sum $N$-player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for…
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 are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout…
This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization…
We consider a class of non-cooperative N-player non-zero-sum stochastic differential games with singular controls, in which each player can affect a linear stochastic differential equation in order to minimize a cost functional which is…
Mean field games (MFG) and mean field control (MFC) problems have been introduced to study large populations of strategic players. They correspond respectively to non-cooperative or cooperative scenarios, where the aim is to find the Nash…
We introduce a new mean field kinetic model for systems of rational agents interacting in a game theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large…