English
Related papers

Related papers: On a Boltzmann mean field model for knowledge grow…

200 papers

In this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas et al [13] to model knowledge growth in an economy. Agents can either increase their knowledge level by exchanging ideas in…

Analysis of PDEs · Mathematics 2016-03-31 Martin Burger , Alexander Lorz , Marie-Therese Wolfram

In this paper we investigate a generalisation of a Boltzmann mean field game (BMFG) for knowledge growth, originally introduced by the economists Lucas and Moll. In BMFG the evolution of the agent density with respect to their knowledge…

Optimization and Control · Mathematics 2023-10-06 Martin Burger , Laura Kanzler , Marie-Therese Wolfram

The Lucas-Moll system is a mean-field game type model describing the growth of an economy by means of diffusion of knowledge. The individual agents in the economy advance their knowledge by learning from each other and via internal…

Analysis of PDEs · Mathematics 2024-09-19 Henri Berestycki , Alexei Novikov , Jean-Michel Roquejoffre , Lenya Ryzhik

Lucas and Moll have proposed a system of forward-backward partial differential equations that model knowledge diffusion and economic growth. It arises from a microscopic model of learning for a mean-field type interacting system of…

Analysis of PDEs · Mathematics 2021-09-22 George Papanicolaou , Lenya Ryzhik , Katerina Velcheva

We analyze a mean-field game model proposed by economists R.E. Lucas and B. Moll (2014) to describe economic systems where production is based on knowledge growth and diffusion. This model reduces to a PDE system where a backward…

Analysis of PDEs · Mathematics 2020-10-22 Alessio Porretta , Luca Rossi

This paper studies the optimal investment behavior of renewable electricity producers in a competitive market, where both prices and installation costs are influenced by aggregate industry activity. We model the resulting crowding effects…

Optimization and Control · Mathematics 2025-07-16 Emma Hubert , Dimitrios Lolas , Ronnie Sircar

This paper develops a mean field game framework for dynamic two-sided matching markets, extending existing matching theory by integrating micro-macro dynamics in two-sided environments. Unlike traditional matching models focusing on static…

Optimization and Control · Mathematics 2026-05-26 Erhan Bayraktar , Dantong Chu , Bohan Li , Ho Man Tai

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

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

We propose a kinetic model to describe the dynamical evolution of wealth and knowledge in national and global markets, starting from a microscopic description of individual interactions. The model is built upon interaction rules that…

Physics and Society · Physics 2026-02-24 Marzia Bisi , Martina Conte , Maria Groppi

Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent…

Analysis of PDEs · Mathematics 2019-07-26 Diogo Gomes , Laurent Lafleche , Levon Nurbekyan

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

We study the mean field games equations, consisting of the coupled Kolmogorov-Fokker-Planck and Hamilton-Jacobi-Bellman equations. The equations are complemented by initial and terminal conditions. It is shown that with some specific choice…

Analysis of PDEs · Mathematics 2019-11-22 Sergey I. Nikulin , Olga S. Rozanova

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…

Probability · Mathematics 2020-11-03 Masaaki Fujii

We consider a Mean Field Games model where the dynamics of the agents is subdiffusive. According to the optimal control interpretation of the problem, we get a system involving fractional time-derivatives for the Hamilton-Jacobi-Bellman and…

Analysis of PDEs · Mathematics 2018-01-23 Fabio Camilli , Raul De Maio

We discuss a class of explicitly solvable mean field type control problems/mean field games with a clear economic interpretation. More precisely, we consider long term average impulse control problems with underlying general one-dimensional…

Optimization and Control · Mathematics 2021-04-28 Sören Christensen , Berenice Anne Neumann , Tobias Sohr

This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…

Optimization and Control · Mathematics 2021-10-12 Xin Guo , Anran Hu , Renyuan Xu , Junzi Zhang

We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the influence of knowledge in the evolution of wealth in a system of agents which interact through the binary trades introduced in Cordier, Pareschi,…

General Finance · Quantitative Finance 2015-06-18 Lorenzo Pareschi , Giuseppe Toscani

This paper studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as…

Optimization and Control · Mathematics 2024-05-06 Zongxia Liang , Keyu Zhang

We consider a constrained hierarchical opinion dynamics in the case of leaders' competition and with complete information among leaders. Each leaders' group tries to drive the followers' opinion towards a desired state accordingly to a…

Optimization and Control · Mathematics 2017-12-12 Giacomo Albi , Lorenzo Pareschi , Mattia Zanella
‹ Prev 1 2 3 10 Next ›