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Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been…

Computer Science and Game Theory · Computer Science 2014-04-08 Hamidou Tembine

The success of modern civilization is built upon widespread cooperation in human society, deciphering the mechanisms behind has being a major goal for centuries. A crucial fact is, however, largely missing in most prior studies that games…

Physics and Society · Physics 2021-06-03 Qinqin Wang , Rizhou Liang , Jiqiang Zhang , Guozhong Zheng , Lin Ma , Li Chen

The goal of the paper is to introduce a set of problems which we call mean field games of timing. We motivate the formulation by a dynamic model of bank run in a continuous-time setting. We briefly review the economic and game theoretic…

Probability · Mathematics 2017-01-24 Rene Carmona , Francois Delarue , Daniel Lacker

Our aim is to model a game for power as a dynamical process, where an excess of power possessed by a player allows him to gain even more power. Such a positive feedback is often termed as the Matthew effect. Analytical and numerical methods…

Using the Minority Game model we study a broad spectrum of problems of market mechanism. We study the role of different types of agents: producers, speculators as well as noise traders. The central issue here is the information flow :…

Statistical Mechanics · Physics 2009-10-31 Damien Challet , Matteo Marsili , Yi-Cheng Zhang

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

In a regular mean field game (MFG), the agents are assumed to be insignificant, they do not realize their effect on the population level and this may result in a phenomenon coined as the Tragedy of the Commons by the economists. However, in…

Optimization and Control · Mathematics 2024-09-13 Gokce Dayanikli , Mathieu Lauriere

This paper presents a simple agent-based model of an economic system, populated by agents playing different games according to their different view about social cohesion and tax payment. After a first set of simulations, correctly…

General Finance · Quantitative Finance 2018-09-24 L. S. Di Mauro , A. Pluchino , A. E. Biondo

This paper describes a basic model of a gift economy in the shape of a Giving Game and reveals the fundamental structure of such a game. Main result is that the game shows a community effect in that a small subgroup of players eventually…

Theoretical Economics · Economics 2021-05-26 Peter Weijland

The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their…

Dynamical Systems · Mathematics 2024-10-24 Kathinka Frieswijk , Lorenzo Zino , Mengbin Ye , Alessandro Rizzo , Ming Cao

Mean field Master equations for the norm game are investigated. The strategies are: to obey the norm or not and to punish those who break it or not. The punishment, the temptation, the punishment cost and the relaxation of vengeance are…

Physics and Society · Physics 2008-02-05 K. Kulakowski

Mean Field Games provide a powerful framework to analyze the dynamics of a large number of controlled objects in interaction. Though these models are much simpler than the underlying differential games they describe in some limit, their…

Physics and Society · Physics 2020-07-15 Thibault Bonnemain , Thierry Gobron , Denis Ullmo

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…

Machine Learning · Computer Science 2026-04-16 Anna C. M. Thöni , Yoram Bachrach , Tal Kachman

This article studies linear-quadratic Stackelberg games between two dominating players (or equivalently, leaders) and a large group of followers, each of whom interacts under a mean field game (MFG) framework. Unlike the conventional…

Optimization and Control · Mathematics 2024-07-02 Dantong Chu , Kenneth Tsz Hin Ng , Sheung Chi Phillip Yam , Harry Zheng

It is a challenging task to reach global cooperation among self-interested agents, which often requires sophisticated design or usage of incentives. For example, we may apply supervisors or referees who are able to detect and punish…

Physics and Society · Physics 2024-12-20 Ting Ling , Zhang Li , Minyu Feng , Attila Szolnoki

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

Knowledge spillovers occur when a firm researches a new technology and that technology is adapted or adopted by another firm, resulting in a social value of the technology that is larger than the initially predicted private value. As a…

Optimization and Control · Mathematics 2021-01-14 Matt Barker , Pierre Degond , Ralf Martin , Mirabelle Muûls

The general picture of game theoretic modeling dealt with here is characterized by a set of big players, also referred to as principals or major agents, acting on the background of large pools of small players, the impact of the behavior of…

Optimization and Control · Mathematics 2019-11-12 Vassili N. Kolokoltsov , Oleg A. Malafeyev

Cooperation and competition between human players in repeated microeconomic games offer a powerful window onto social phenomena such as the establishment, breakdown and repair of trust. This offers the prospect of particular insight into…

Neurons and Cognition · Quantitative Biology 2018-07-04 Andreas Hula , Iris Vilares , Peter Dayan , P. Read Montague

Mean field games and controls involve guiding the behavior of large populations of interacting agents, where each individual's influence on the group is negligible but collectively impacts overall dynamics. Hybrid systems integrate…

Optimization and Control · Mathematics 2024-12-17 Tejaswi K. C. , Taeyoung Lee