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Related papers: 'Phase diagram' of a mean field game

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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…

Optimization and Control · Mathematics 2024-06-18 Gokce Dayanikli , Mathieu Lauriere

Mean field theory provides an effective way of scaling multiagent reinforcement learning algorithms to environments with many agents that can be abstracted by a virtual mean agent. In this paper, we extend mean field multiagent algorithms…

Multiagent Systems · Computer Science 2022-06-22 Sriram Ganapathi Subramanian , Pascal Poupart , Matthew E. Taylor , Nidhi Hegde

The dynamics of minority games with agents trading on different time scales is studied via dynamical mean-field theory. We analyze the case where the agents' decision-making process is deterministic and its stochastic generalization with…

Disordered Systems and Neural Networks · Physics 2009-11-10 Andrea De Martino

We study a toy model of linear-quadratic mean field game with delay. We "lift" the delayed dynamic into an infinite dimensional space, and recast the mean field game system which is made of a forward Kolmogorov equation and a backward…

Probability · Mathematics 2018-08-21 Jean-Pierre Fouque , Zhaoyu Zhang

Motivated by models of epidemic control in large populations, we consider a Stackelberg mean field game model between a principal and a mean field of agents evolving on a finite state space. The agents play a non-cooperative game in which…

Optimization and Control · Mathematics 2021-05-26 Alexander Aurell , Rene Carmona , Gokce Dayanikli , Mathieu Lauriere

In this paper, we investigate the mean field games with $K$ classes of agents who are weakly coupled via the empirical measure. The underlying dynamics of the representative agents is assumed to be a controlled nonlinear Markov process…

Probability · Mathematics 2012-04-09 Vassili N. Kolokoltsov , Jiajie Li , Wei Yang

This paper is interested in the problem of optimal stopping in a mean field game context. The notion of mixed solution is introduced to solve the system of partial differential equations which models this kind of problem. This notion…

Analysis of PDEs · Mathematics 2017-06-14 C. Bertucci

We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity,…

Analysis of PDEs · Mathematics 2020-06-24 Z Kobeissi

This article introduces a novel mean-field game model for multi-sector economic growth in which a dynamically evolving externality, influenced by the collective actions of agents, plays a central role. Building on classical growth theories…

Optimization and Control · Mathematics 2026-05-05 Pierre Lavigne , Quentin Petit , Xavier Warin

In this paper we propose two new monotonicity conditions that could serve as sufficient conditions for uniqueness of Nash equilibria in mean field games. In this study we aim for $unconditional\ uniqueness$ that is independent of the length…

Analysis of PDEs · Mathematics 2023-07-24 P. Jameson Graber , Alpár R. Mészáros

We initiate the analysis of the response of computer owners to various offers of defence systems against a cyber-hacker (for instance, a botnet attack), as a stochastic game of a large number of interacting agents. We introduce a simple…

Optimization and Control · Mathematics 2022-05-03 Vassili Kolokoltsov , Alain Bensoussan

In this paper, we study a class of linear-quadratic (LQ) mean field games of controls with common noises and their corresponding $N$-player games. The theory of mean field game of controls considers a class of mean field games where the…

Optimization and Control · Mathematics 2022-06-13 Min Li , Chenchen Mou , Zhen Wu , Chao Zhou

The purpose of this work is to pose and solve the problem to guide a collection of weakly interacting dynamical systems (agents, particles, etc.) to a specified terminal distribution. The framework is that of mean-field and of cooperative…

Systems and Control · Computer Science 2017-12-12 Yongxin Chen , Tryphon T. Georgiou , Michele Pavon

We introduce a zero-sum game problem of mean-field type as an extension of the classical zero-sum Dynkin game problem to the case where the payoff processes might depend on the value of the game and its probability law. We establish…

Optimization and Control · Mathematics 2022-05-06 Boualem Djehiche , Roxana Dumitrescu

In this paper, we investigate the interaction of two populations with a large number of indistinguishable agents. The problem consists in two levels: the interaction between agents of a same population, and the interaction between the two…

Optimization and Control · Mathematics 2018-10-30 Alain Bensoussan , Tao Huang , Mathieu Laurière

The recently developed mean-field game models of corruption and bot-net defence in cyber-security, the evolutionary game approach to inspection and corruption, and the pressure-resistance game element, can be combined under an extended…

Optimization and Control · Mathematics 2022-05-03 Stamatios Katsikas , Vassili Kolokoltsov

In this article we study the well-posedness of the Master Equation of Mean Field Games in a framework of Neumann boundary condition. The definition of solution is closely related to the classical one of the Mean Field Games system, but the…

Analysis of PDEs · Mathematics 2021-05-19 Michele Ricciardi

Finite mixture models are an important tool in the statistical analysis of data, for example in data clustering. The optimal parameters of a mixture model are usually computed by maximizing the log-likelihood functional via the…

Machine Learning · Statistics 2020-11-30 Laura Aquilanti , Simone Cacace , Fabio Camilli , Raul De Maio

We establish a connection between federated learning, a concept from machine learning, and mean-field games, a concept from game theory and control theory. In this analogy, the local federated learners are considered as the players and the…

Machine Learning · Statistics 2021-07-09 Arash Mehrjou

This paper studies the relation between equilibria in single-period, discrete-time and continuous-time mean field game models. First, for single-period mean field games, we establish the existence of equilibria and then prove the…

Optimization and Control · Mathematics 2024-11-04 Jodi Dianetti , Max Nendel , Ludovic Tangpi , Shichun Wang