Related papers: Constrained Mean Field Games with Grushin type dyn…
In this paper, we study a class of discrete-time mean-field games under the infinite-horizon risk-sensitive discounted-cost optimality criterion. Risk-sensitivity is introduced for each agent (player) via an exponential utility function. In…
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary…
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…
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…
We introduce a general probabilistic framework for discrete-time, infinite-horizon discounted Mean Field Type Games (MFTGs) with both global common noise and team-specific common noises. In our model, agents are allowed to use randomized…
A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population.…
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…
We study first order evolutive Mean Field Games where the Hamiltonian is non-coercive. This situation occurs, for instance, when some directions are "forbidden" to the generic player at some points. We establish the existence of a weak…
We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…
In a probabilistic mean field game driven by a L\'evy process an individual player aims to minimize a long run discounted/ergodic cost by controlling the process through a pair of increasing and decreasing c\`adl\`ag processes, while he is…
We consider time-dependent viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in mean-field game theory, and describe Nash equilibria of games with a large number of agents aiming…
We study first order evolutive Mean Field Games whose operators are non-coercive. This situation occurs, for instance, when some directions are `forbidden' to the generic player at some points. Under some regularity assumptions, we…
We study the existence of classical solutions to a broad class of local, first order, forward-backward Extended Mean Field Games systems, that includes standard Mean Field Games, Mean Field Games with congestion, and mean field type control…
We consider finite horizon stochastic mean field games in which the state space is a network. They are described by a system coupling a backward in time Hamilton-Jacobi-Bellman equation and a forward in time Fokker-Planck equation. The…
Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, while minimizing a cost. The optimal transition rates are…
This paper focuses on the role of a government of a large population of interacting agents as a mean field optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a PDE of…
In this paper, we examine the stationary relaxed singular control problem within a multi-dimensional framework for a single agent, as well as its mean field game equivalent. We demonstrate that optimal relaxed controls exist for two problem…
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…
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…
Motivated by recent interest in graphon mean field games and their applications, this paper provides a comprehensive probabilistic analysis of graphon mean field control (GMFC) problems, where the controlled dynamics are governed by a…