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Related papers: A duality approach to a price formation MFG model

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We consider the mean-field game price formation model introduced by Gomes and Sa\'ude. In this MFG model, agents trade a commodity whose supply can be deterministic or stochastic. Agents maximize profit, taking into account current and…

Numerical Analysis · Mathematics 2022-04-05 Yuri Ashrafyan , Tigran Bakaryan , Diogo Gomes , Julian Gutierrez

In this paper, we study a class of first-order mean-field games (MFGs) that model price formation. Using Poincar{\'e} Lemma, we eliminate one of the equations and obtain a variational problem for a single function. This variational problem…

Analysis of PDEs · Mathematics 2022-04-05 Yuri Ashrafyan , Tigran Bakaryan , Diogo Gomes , Julian Gutierrez

We propose and investigate a general class of discrete time and finite state space mean field game (MFG) problems with potential structure. Our model incorporates interactions through a congestion term and a price variable. It also allows…

Optimization and Control · Mathematics 2023-03-07 J. Frédéric Bonnans , Pierre Lavigne , Laurent Pfeiffer

Here, we introduce a price-formation model where a large number of small players can store and trade electricity. Our model is a constrained mean-field game (MFG) where the price is a Lagrange multiplier for the supply vs. demand balance…

Analysis of PDEs · Mathematics 2018-07-20 Diogo Gomes , João Saúde

In this paper, we propose a mean-field game model for the price formation of a commodity whose production is subjected to random fluctuations. The model generalizes existing deterministic price formation models. Agents seek to minimize…

Analysis of PDEs · Mathematics 2020-03-05 Diogo Gomes , Julian Gutierrez , Ricardo Ribeiro

Here, we examine a fully-discrete Semi-Lagrangian scheme for a mean-field game price formation model. We show the existence of the solution of the discretized problem and that it is monotone as a multivalued operator. Moreover, we show that…

Numerical Analysis · Mathematics 2025-01-31 Yuri Ashrafyan , Diogo Gomes

Here, we observe that mean-field game (MFG) systems admit a two-player infinite-dimensional general-sum differential game formulation. We show that particular regimes of this game reduce to previously known variational principles.…

Analysis of PDEs · Mathematics 2018-04-25 Marco Cirant , Levon Nurbekyan

We propose two novel frameworks to study the price formation of an asset negotiated in an order book. Specifically, we develop a game-theoretic model in many-person games and mean-field games, considering costs stemming from limited…

Trading and Market Microstructure · Quantitative Finance 2022-02-24 David Evangelista , Yuri Saporito , Yuri Thamsten

We consider a market where a finite number of players trade an asset whose supply is a stochastic process. The price formation problem consists of finding a price process that ensures that when agents act optimally to minimize their trading…

Analysis of PDEs · Mathematics 2022-08-15 Diogo Gomes , Julian Gutierrez , Ricardo Ribeiro

This paper investigates the simultaneous reconstruction of the running cost function and the internal topological structure within the mean-field games (MFG) system utilizing partial boundary data. The inverse problem is notably challenging…

Optimization and Control · Mathematics 2024-08-20 Ming-Hui Ding , Hongyu Liu , Guang-Hui Zheng

This paper analyzes a class of infinite-time-horizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the mean-field game (MFG) and presents sensitivity analysis…

Optimization and Control · Mathematics 2020-08-12 Haoyang Cao , Xin Guo

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard…

Numerical Analysis · Mathematics 2017-05-02 Diogo Gomes , Joao Saude

In this paper, we propose and study an inverse boundary problem for the mean field games (MFGs) governed by the first-order master equation in a bounded domain. We establish the unique identifiability result by showing that the running cost…

Analysis of PDEs · Mathematics 2022-12-21 Hongyu Liu , Shen Zhang

We propose a machine learning method to solve a mean-field game price formation model with common noise. This involves determining the price of a commodity traded among rational agents subject to a market clearing condition imposed by…

Optimization and Control · Mathematics 2023-05-30 Diogo Gomes , Julian Gutierrez , Mathieu Laurière

We consider the variational structure of a time-fractional second order Mean Field Games (MFG) system with local coupling. The MFG system consists of time-fractional Fokker-Planck and Hamilton-Jacobi-Bellman equations. In such a situation…

Analysis of PDEs · Mathematics 2019-07-03 Tang Qing , Fabio Camilli

In this paper, we propose and study the utilization of the Dirichlet-to-Neumann (DN) map to uniquely identify the discount functions $r, k$ and cost function $F$ in a stationary mean field game (MFG) system. This study features several…

Optimization and Control · Mathematics 2023-08-15 Ming-Hui Ding , Hongyu Liu , Guang-Hui Zheng

Here, we study the existence and the convergence of solutions for the vanishing discount MFG problem with a quadratic Hamiltonian. We give conditions under which the discounted problem has a unique classical solution and prove convergence…

Analysis of PDEs · Mathematics 2019-08-20 Diogo A. Gomes , Hiroyoshi Mitake , Kengo Terai

This chapter examines monotonicity techniques in the theory of mean-field games(MFGs). Originally, monotonicity ideas were used to establish the uniqueness of solutions for MFGs. Later, monotonicity methods and monotone operators were…

Analysis of PDEs · Mathematics 2025-02-28 Rita Ferreira , Diogo Gomes , Teruo Tada

In this paper we formulate the now classical problem of optimal liquidation (or optimal trading) inside a Mean Field Game (MFG). This is a noticeable change since usually mathematical frameworks focus on one large trader in front of a…

Trading and Market Microstructure · Quantitative Finance 2017-09-22 Pierre Cardaliaguet , Charles-Albert Lehalle

For two classes of Mean Field Game systems we study the convergence of solutions as the interest rate in the cost functional becomes very large, modeling agents caring only about a very short time-horizon, and the cost of the control…

Optimization and Control · Mathematics 2020-04-10 Martino Bardi , Pierre Cardaliaguet
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