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Reinforcement learning is a powerful tool to learn the optimal policy of possibly multiple agents by interacting with the environment. As the number of agents grow to be very large, the system can be approximated by a mean-field problem.…
Quantum games represent the really 21st century branch of game theory, tightly linked to the modern development of quantum computing and quantum technologies. The main accent in these developments so far was made on stationary or repeated…
In a game theoretic framework, we study energy markets with a continuum of homogenous producers who produce energy from an exhaustible resource such as oil. Each producer simultaneously optimizes production rate that drives her revenues, as…
This work establishes the equivalence between Mean Field Game and a class of PDE systems closely related to compressible Navier-Stokes equations. The solvability of the PDE system via the existence of the Nash Equilibrium of the Mean Field…
The theory of Mean Field Game of Controls considers a class of mean field games where the interaction is through the joint distribution of the state and control. It is well known that, for standard mean field games, certain monotonicity…
This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop Nash equilibria are introduced. Existence of an open-loop Nash equilibrium…
This paper investigates an indefinite linear-quadratic partially observed mean-field game with common noise, incorporating both state-average and control-average effects. In our model, each agent's state is observed through both individual…
We study mean field games for large non--exchangeable populations with moderate local interactions and common noise. The finite--player system is driven by two complementary interaction mechanisms : a graphon--type structure, which encodes…
This paper studies a class of linear quadratic mean field games where the coefficients of quadratic cost functions depend on both the mean and the variance of the population's state distribution through its quantile function. Such a…
Mean field games allow to describe tractable models of dynamic games with a continuum of players, explicit interaction and heterogeneous states. Thus, these models are of great interest for socio-economic applications. A particular class of…
Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…
The goal of this paper is to study a Mean Field Game (MFG) system stemming from the harvesting of resources. Modelling the latter through a reaction-diffusion equation and the harvesters as competing rational agents, we are led to a…
We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on…
The goal of the paper is to introduce a formulation of the mean field game with major and minor players as a fixed point on a space of controls. This approach emphasizes naturally the role played by McKean-Vlasov dynamics in some of the…
This paper is concerned with non-zero sum differential games of mean-field stochastic differential equations with partial information and convex control domain. First, applying the classical convex variations, we obtain stochastic maximum…
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,…
This paper revisits well-studied dynamic decisions of weakly coupled large-population (LP) systems. Specifically, three types of LP decision problems: mean-field game (MG), mean-field team (MT), and mean-field-type control (MC), are…
Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and…
In this paper, we consider a mean field game model inspired by crowd motion in which several interacting populations evolving in $\mathbb R^d$ aim at reaching given target sets in minimal time. The movement of each agent is described by a…
Mean field games (MFG) and mean field control problems (MFC) are frameworks to study Nash equilibria or social optima in games with a continuum of agents. These problems can be used to approximate competitive or cooperative games with a…