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Related papers: Forecasting Public Sentiments via Mean Field Games

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Here, we consider one-dimensional forward-forward mean-field games (MFGs) with congestion, which were introduced to approximate stationary MFGs. We use methods from the theory of conservation laws to examine the qualitative properties of…

Analysis of PDEs · Mathematics 2017-03-30 Diogo Gomes , Marc Sedjro

The paper studies the convergence, as $N$ tends to infinity, of a system of $N$ coupled Hamilton-Jacobi equations, the Nash system. This system arises in differential game theory. We describe the limit problem in terms of the so-called…

Analysis of PDEs · Mathematics 2015-09-09 Pierre Cardaliaguet , François Delarue , Jean-Michel Lasry , Pierre-Louis Lions

We present a linear--quadratic Stackelberg game with a large number of followers and we also derive the mean field limit of infinitely many followers. The relation between optimization and mean-field limit is studied and conditions for…

Optimization and Control · Mathematics 2020-11-09 Michael Herty , Sonja Steffensen , Anna Thünen

We consider a model of cultural evolution for a strategy selection in a population of individuals who interact in a game theoretic framework. The evolution combines individual learning of the environment (population strategy profile),…

Populations and Evolution · Quantitative Biology 2020-06-03 Misha Perepelitsa

We present a quantitative theory, based on crowd effects, for the market volatility in a Minority Game played by a mixed population. Below a critical concentration of generalized strategy players, we find that the volatility in the crowded…

Condensed Matter · Physics 2009-10-31 P. Jefferies , M. Hart , N. F. Johnson , P. M. Hui

We consider a class of optimal control problems that arise in connection with optimal advertising under uncertainty. Two main features appear in the model: a delay in the control variable driving the state dynamics; a mean-field term both…

Optimization and Control · Mathematics 2024-03-04 Michele Ricciardi , Mauro Rosestolato

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…

Probability · Mathematics 2014-09-26 Rene Carmona , Xiuneng Zhu

Mean Field inference is central to statistical physics. It has attracted much interest in the Computer Vision community to efficiently solve problems expressible in terms of large Conditional Random Fields. However, since it models the…

Computer Vision and Pattern Recognition · Computer Science 2016-11-24 Pierre Baqué , François Fleuret , Pascal Fua

Mean-field games (MFGs) are a modeling framework for systems with a large number of interacting agents. They have applications in economics, finance, and game theory. Normalizing flows (NFs) are a family of deep generative models that…

Optimization and Control · Mathematics 2023-05-24 Han Huang , Jiajia Yu , Jie Chen , Rongjie Lai

We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious…

Optimization and Control · Mathematics 2023-08-22 Pierre Lavigne , Laurent Pfeiffer

In computational reinforcement learning, a growing body of work seeks to express an agent's model of the world through predictions about future sensations. In this manuscript we focus on predictions expressed as General Value Functions:…

Machine Learning · Computer Science 2021-11-23 Alex Kearney , Anna Koop , Johannes Günther , Patrick M. Pilarski

We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower…

Artificial Intelligence · Computer Science 2009-09-25 L. K. Saul , T. Jaakkola , M. I. Jordan

In this paper, we consider mean-field games where the interaction of each player with the mean-field takes into account not only the states of the players but also their collective behavior, To do so, we develop a random variable framework…

Analysis of PDEs · Mathematics 2015-06-23 Diogo A. Gomes , Vardan K. Voskanyan

A mean-field game (MFG) seeks the Nash Equilibrium of a game involving a continuum of players, where the Nash Equilibrium corresponds to a fixed point of the best-response mapping. However, simple fixed-point iterations do not always…

Optimization and Control · Mathematics 2025-07-15 Jiajia Yu , Xiuyuan Cheng , Jian-Guo Liu , Hongkai Zhao

We consider the task of forecasting an infinite sequence of future observations based on some number of past observations, where the probability measure generating the observations is "suspected" to satisfy one or more of a set of…

Machine Learning · Computer Science 2019-05-17 Vanessa Kosoy

In many stochastic games stemming from financial models, the environment evolves with latent factors and there may be common noise across agents' states. Two classic examples are: (i) multi-agent trading on electronic exchanges, and (ii)…

Optimization and Control · Mathematics 2019-07-24 Dena Firoozi , Peter E. Caines , Sebastian Jaimungal

In this work we discuss an Mean Field Games approach to traffic management on multi-lane roads. Such approach is particularly indicated to model self driven vehicles with perfect information of the domain. The mathematical interest of the…

Optimization and Control · Mathematics 2018-05-14 Adriano Festa , Simone Göttlich

In this paper we use a minimal model based on Mean-Field Games (a mathematical framework apt to describe situations where a large number of agents compete strategically) to simulate the scenario where a static dense human crowd is crossed…

Physics and Society · Physics 2024-05-29 Matteo Butano , Thibault Bonnemain , Cécile Appert-Rolland , Alexandre Nicolas , Denis Ullmo

We consider a deterministic mean field games problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect…

Optimization and Control · Mathematics 2023-05-03 Justina Gianatti , Francisco J. Silva , Ahmad Zorkot

This paper focuses on a model for opinion dynamics, where the influence weights of agents evolve in time. We formulate a control problem of consensus type, in which the objective is to drive all agents to a final target point under suitable…

Analysis of PDEs · Mathematics 2020-11-10 Nastassia Duteil , Benedetto Piccoli