Related papers: On Discounted Infinite-Time Mean Field Games
In the context of large population symmetric games, approximate Nash equilibria are introduced through equilibrium solutions of the corresponding mean field game in the sense that the individual gain from optimal unilateral deviation under…
Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…
This paper studies social optima and Nash games for mean field linear quadratic control systems, where subsystems are coupled via dynamics and individual costs. For the social control problem, we first obtain a set of forward-backward…
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…
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 prove the global-in-time well-posedness for a broad class of mean field game problems, which is beyond the special linear-quadratic setting, as long as the mean field sensitivity is not too large. Through the stochastic maximum…
In [17], we introduced the discounted infinite-time mean field games. Subsequently, in [18], we studied the connection between infinite-time mean field FBSDEs and elliptic master equations. In this paper, we further investigate the…
We propose a stochastic game modelling the strategic interaction between market makers and traders of optimal execution type. For traders, the permanent price impact commonly attributed to them is replaced by quoting strategies implemented…
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…
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…
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…
The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…
Mean-field games (MFG) were introduced to efficiently analyze approximate Nash equilibria in large population settings. In this work, we consider entropy-regularized mean-field games with a finite state-action space in a discrete time…
We consider a general class of finite-player stochastic games with mean-field interaction, in which the linear-quadratic cost functional includes linear operators acting on controls in $L^2$. We propose a novel approach for deriving the…
Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where…
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…
This paper studies relative arbitrage opportunities in a market with competitive investors through stochastic differential games in the limit as the number of players tends to infinity. With common noises introduced by the stock…
We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games…
Mean field games (MFGs) model equilibria in games with a continuum of weakly interacting players as limiting systems of symmetric $n$-player games. We consider the finite-state, infinite-horizon problem with ergodic cost. Assuming Markovian…
We study stochastic mean-field games among finite number of teams with large finite as well as infinite number of decision makers. For this class of games within static and dynamic settings, we establish the existence of a Nash equilibrium,…