Related papers: High-dimensional Mean-Field Games by Particle-base…
Mean field games (MFGs) model interactions in large-population multi-agent systems through population distributions. Traditional learning methods for MFGs are based on fixed-point iteration (FPI), where policy updates and induced population…
Finding Nash equilibria in two-player zero-sum continuous games is a central problem in machine learning, e.g. for training both GANs and robust models. The existence of pure Nash equilibria requires strong conditions which are not…
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…
In this article, we study the global-in-time well-posedness of second order mean field games (MFGs) with both nonlinear drift functions simultaneously depending on the state, distribution and control variables, and the diffusion term…
This paper proposes a novel method, Explicit Flow Matching (ExFM), for training and analyzing flow-based generative models. ExFM leverages a theoretically grounded loss function, ExFM loss (a tractable form of Flow Matching (FM) loss), to…
Flow matching (FM) has gained significant attention as a simulation-free generative model. Unlike diffusion models, which are based on stochastic differential equations, FM employs a simpler approach by solving an ordinary differential…
Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading…
The theory of Mean-Field Games is interested in the behaviour of interacting particle systems in which the individual interaction between particles (players) decreases as the size of the population increases. In recent years, it was…
This paper discusses the control of coherent structures in turbulent flows, which has broad applications among complex systems in science and technology. Mean field games have been proved a powerful tool and are proposed here to control the…
The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost…
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…
Mean Field Game (MFG) models implicitly assume "rational expectations", meaning that the heterogeneous agents being modeled correctly know all relevant transition probabilities for the complex system they inhabit. When there is common…
This paper proposes and analyzes two neural network methods to solve the master equation for finite-state mean field games (MFGs). Solving MFGs provides approximate Nash equilibria for stochastic, differential games with finite but large…
Financial markets and more generally macro-economic models involve a large number of individuals interacting through variables such as prices resulting from the aggregate behavior of all the agents. Mean field games have been introduced to…
We extend the weak-strong uniqueness principle for mean-field game (MFG) systems to a broad class of second-order stationary and time-dependent problems. Under standard monotonicity, growth, and coercivity assumptions on the Hamiltonian,…
Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely large populations of agents. Yet, most of the literature assumes a single initial distribution for the agents, which limits the practical applications of MFGs.…
Here, we examine the Wardrop equilibrium model on networks with flow-dependent costs and its connection with stationary mean-field games (MFG). In the first part of this paper, we present the Wardrop and the first-order MFG models on…
The simulation of high-energy physics collision events is a key element for data analysis at present and future particle accelerators. The comparison of simulation predictions to data allows looking for rare deviations that can be due to…
We introduce Mean-Field Trust Region Policy Optimization (MF-TRPO), a novel algorithm designed to compute approximate Nash equilibria for ergodic Mean-Field Games (MFG) in finite state-action spaces. Building on the well-established…
Conventional Mean-field games/control study the behavior of a large number of rational agents moving in the Euclidean spaces. In this work, we explore the mean-field games on Riemannian manifolds. We formulate the mean-field game Nash…