Related papers: Multi-population Mean Field Games with Multiple Ma…
We consider a continuum of carbon-emitting firms who seek to maximise their stock price, and a regulator (e.g., Government) who wishes for the economy to flourish, whilst simultaneously punishing firms who behave non-green. Interpreting the…
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…
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…
The most serious threat to ecosystems is the global climate change fueled by the uncontrolled increase in carbon emissions. In this project, we use mean field control and mean field game models to analyze and inform the decisions of…
For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then,…
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…
The goal of the paper is to develop the theory of finite state mean field games with major and minor players when the state space of the game is finite. We introduce the finite player games and derive a mean field game formulation in the…
We investigate a stochastic differential game in which a major player has a private information (the knowledge of a random variable), which she discloses through her control to a population of small players playing in a Nash Mean Field 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…
Mean Field Games (MFG) have been introduced to tackle games with a large number of competing players. Considering the limit when the number of players is infinite, Nash equilibria are studied by considering the interaction of a typical…
In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…
We investigate how the framework of mean-field games may be used to investigate strategic interactions in large heterogeneous populations. We consider strategic interactions in a population of players which may be partitioned into…
In this paper, we consider a mean field game (MFG) with a major and $N$ minor agents. We first consider the limiting problem and allow the coefficients to vary with the conditional distribution in a nonlinear way. We use the stochastic…
This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…
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 (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 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…
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the…
We introduce a simple class of mean field games with absorbing boundary over a finite time horizon. In the corresponding $N$-player games, the evolution of players' states is described by a system of weakly interacting It\^o equations with…
One of the contributions of this work is to formulate the problem of energy-efficient power control in multiple access channels (namely, channels which comprise several transmitters and one receiver) as a stochastic differential game. The…