Related papers: Deep Learning for Mean Field Games and Mean Field …
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…
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…
We propose a mean field control game model for the intra-and-inter-bank borrowing and lending problem. This framework allows to study the competitive game arising between groups of collaborative banks. The solution is provided in terms of…
In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…
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…
Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…
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…
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…
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…
We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…
Mean field games are limit models for symmetric $N$-player games with interaction of mean field type as $N\to\infty$. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate…
In this paper, we propose a numerical methodology for finding the closed-loop Nash equilibrium of stochastic delay differential games through deep learning. These games are prevalent in finance and economics where multi-agent interaction…
This is an expanded version of the lecture given at the AMS Short Course on Mean Field Games, on January 13, 2020 in Denver CO. The assignment was to discuss applications of Mean Field Games in finance and economics. I need to admit upfront…
Stochastic optimal control and games have a wide range of applications, from finance and economics to social sciences, robotics, and energy management. Many real-world applications involve complex models that have driven the development of…
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…
Deciding bank interest rates has been a long-standing challenge in finance. It is crucial to ensure that the selected rates balance market share and profitability. However, traditional approaches typically focus on the interest rate changes…
We present a new combined \textit{mean field control game} (MFCG) problem which can be interpreted as a competitive game between collaborating groups and its solution as a Nash equilibrium between groups. Players coordinate their strategies…
We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…
Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malham\'e, Mean…