Game theory | Mathematical economics
Mean-field game theory is the study of strategic decision making by small interacting agents in very large populations. Use of the term "mean field" is inspired by mean-field theory in physics, which considers the behaviour of systems of large numbers of particles where individual particles have negligible impact upon the system. This class of problems was considered in the economics literature by Boyan Jovanovic and Robert W. Rosenthal, in the engineering literature by Minyi Huang, Roland Malhame, and Peter E. Caines and independently and around the same time by mathematicians and Pierre-Louis Lions. In continuous time a mean-field game is typically composed by a Hamilton–Jacobi–Bellman equation that describes the optimal control problem of an individual and a Fokker–Planck equation that describes the dynamics of the aggregate distribution of agents. Under fairly general assumptions it can be proved that a class of mean-field games is the limit as of an N-player Nash equilibrium. A related concept to that of mean-field games is "mean-field-type control". In this case a social planner controls a distribution of states and chooses a control strategy. The solution to a mean-field-type control problem can typically be expressed as dual adjoint Hamilton–Jacobi–Bellman equation coupled with Kolmogorov equation. Mean-field-type game theory is the multi-agent generalization of the single-agent mean-field-type control. (Wikipedia).
Jules Hedges - compositional game theory - part I
Compositional game theory is an approach to game theory that is designed to have better mathematical (loosely “algebraic” and “geometric”) properties, while also being intended as a practical setting for microeconomic modelling. It gives a graphical representation of games in which the flo
From playlist compositional game theory
Definition of a Field In this video, I define the concept of a field, which is basically any set where you can add, subtract, add, and divide things. Then I show some neat properties that have to be true in fields. Enjoy! What is an Ordered Field: https://youtu.be/6mc5E6x7FMQ Check out
From playlist Real Numbers
Physics - E&M: Ch 36.1 The Electric Field Understood (1 of 17) What is an Electric Field?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is an electric field. An electric field exerts a force on a charged place in the field, can be detected by placing a charged in the field and observing the effect on the charge. The stren
From playlist THE "WHAT IS" PLAYLIST
Tembine Hamidou: "Mean-Field-Type Games"
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop III: Mean Field Games and Applications "Mean-Field-Type Games" Tembine Hamidou - New York University Abstract: A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
Field Definition (expanded) - Abstract Algebra
The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They
From playlist Abstract Algebra
Yves Achdou - Some recent contributions on mean field games
Yves Achdou (Université Paris Diderot) In 2007, J-M. Lasry and P.-L. Lions proposed mean field-type models to study differential games with a large number of players. We will discuss several variants of these models, in particular stochastic optimal control problems with mean-field eff
From playlist Schlumberger workshop on Topics in Applied Probability
Peter Caines: "Graphon MFGs: A Dynamical Equilibrium Theory for Large Populations on Large Scale..."
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop III: Mean Field Games and Applications "Graphon Mean Field Games: A Dynamical Equilibrium Theory for Large Populations on Large Scale Networks" Peter Caines - McGill University Abstract: Very large scale (finite) networks (VLSNs) linkin
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
Jianfeng Zhang: "Set Values for Mean Field Games with Multiple Equilibriums"
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop III: Mean Field Games and Applications "Set Values for Mean Field Games with Multiple Equilibriums" Jianfeng Zhang - University of Southern California (USC) Abstract: It is well known that a mean field game under the monotonicity condit
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
What Is a Field? - Instant Egghead #42
Contributing editor George Musser explains how physicists think about the universe using the fundamental concept of "the field". -- WATCH more Instant Egghead: http://goo.gl/CkXwKj SUBSCRIBE to our channel: http://goo.gl/fmoXZ VISIT ScientificAmerican.com for the latest science news:http
From playlist Quantum Field Theory
Cohesive Games and Lessons Learned from the Field Theory of Games
Based on teaching the Field Theory of Games to upper-class students, there were interesting lessons learned. For example, it is possible in a short time to educate them to use the Wolfram Language sufficiently to apply the field theory of games to problems of interest to them. It is possib
From playlist Wolfram Technology Conference 2022
Peter E. Caines: Graphon Mean Field Games and the GMFG Equations
Very large networks linking dynamical agents are now ubiquitous and there is significant interest in their analysis, design and control. The emergence of the graphon theory of large networks and their infinite limits has recently enabled the formulation of a theory of the centralized contr
From playlist Probability and Statistics
Quantum field theory, Lecture 2
This winter semester (2016-2017) I am giving a course on quantum field theory. This course is intended for theorists with familiarity with advanced quantum mechanics and statistical physics. The main objective is introduce the building blocks of quantum electrodynamics. Here in Lecture 2
From playlist Quantum Field Theory
Multi Type Mean Field Reinforcement Learning | AISC
For slides and more information on the paper, visit https://ai.science/e/multi-type-mean-field-reinforcement-learning--ZPQxNPfeGM02aiyTqViE Discussion lead: Sriram Ganapathi Subramanian, Matthew Taylor This paper presents scaling up RL to hundreds or thousands of agents using a "mean fie
From playlist Reinforcement Learning
Modified Navier–Stokes and Decision Process Theory
As a next step in investigating decision process theory, Jerry Thomas considers steady-state non-streamline solutions to a 3D model. The equations are modified Navier–Stokes equations. Using NDSolve, he shows that these steady-state solutions are not dissimilar to fluid flow solutions desp
From playlist Wolfram Technology Conference 2020
Tamer Başar: "A General Theory for Discrete-Time Mean-Field Games"
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop III: Mean Field Games and Applications "A General Theory for Discrete-Time Mean-Field Games" Tamer Başar - University of Illinois at Urbana-Champaign Abstract: In this lecture, I will present a general theory for mean-field games formul
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
Session 2 - Field theory as a string theory: Timothy adamo
https://strings2015.icts.res.in/talkTitles.php
From playlist Strings 2015 conference
Algorithmic Game Theory by Siddharth Barman
Program Summer Research Program on Dynamics of Complex Systems ORGANIZERS: Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE : 15 May 2019 to 12 July 2019 VENUE : Madhava hall for Summer School & Ramanujan hall f
From playlist Summer Research Program On Dynamics Of Complex Systems 2019
Chris Miller: Expansions of the real field by trajectories of definable vector fields
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
F. Santambrogio - Optimal Control, Differential Games, Mean Field Games, ...
Optimal Control, Differential Games, Mean Field Games, and Pontryagin and Hamilton-Jacobi equations on probabilities The talk will be a short introduction to the emerging topic of Mean Field Games in connection with optimal control and differential games. I will present what is in general
From playlist Journées Sous-Riemanniennes 2017