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Related papers: Inverse problems for mean field games

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The objective of this paper is to analyze the existence of equilibria for a class of deterministic mean field games of controls. The interaction between players is due to both a congestion term and a price function which depends on the…

Optimization and Control · Mathematics 2022-01-19 Joseph Frédéric Bonnans , Justina Gianatti , Laurent Pfeiffer

We propose the concept of a Lagrangian game to solve constrained Markov games. Such games model scenarios where agents face cost constraints in addition to their individual rewards, that depend on both agent joint actions and the evolving…

Optimization and Control · Mathematics 2025-03-14 Soham Das , Santiago Paternain , Luiz F. O. Chamon , Ceyhun Eksin

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

The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…

Optimization and Control · Mathematics 2020-03-11 Yves Achdou , Mathieu Laurière

By following the study in [24], we consider an inverse boundary problem for the mean field game system where a probability density constraint is enforced on the game agents. That is, we consider the case that reflective boundary conditions…

Analysis of PDEs · Mathematics 2024-02-22 Hongyu Liu , Shen Zhang

Designing suitable reward functions for numerous interacting intelligent agents is challenging in real-world applications. Inverse reinforcement learning (IRL) in mean field games (MFGs) offers a practical framework to infer reward…

Machine Learning · Computer Science 2025-09-05 Yang Chen , Xiao Lin , Bo Yan , Libo Zhang , Jiamou Liu , Neset Özkan Tan , Michael Witbrock

In an inverse game problem, one needs to infer the cost function of the players in a game such that a desired joint strategy is a Nash equilibrium. We study the inverse game problem for a class of multiplayer matrix games, where the cost…

Computer Science and Game Theory · Computer Science 2022-10-17 Yue Yu , Jonathan Salfity , David Fridovich-Keil , Ufuk Topcu

Mean field games are limit models for symmetric $N$-player games with interaction of mean field type as $N\to\infty$. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate…

Probability · Mathematics 2017-05-29 Markus Fischer

In this paper, we study inverse game theory (resp. inverse multiagent learning) in which the goal is to find parameters of a game's payoff functions for which the expected (resp. sampled) behavior is an equilibrium. We formulate these…

Computer Science and Game Theory · Computer Science 2025-02-21 Denizalp Goktas , Amy Greenwald , Sadie Zhao , Alec Koppel , Sumitra Ganesh

This paper is devoted to finite horizon deterministic mean field games in which the state space is a network. The agents control their velocity, and when they occupy a vertex, they can enter into any incident edge. The running and terminal…

Optimization and Control · Mathematics 2023-11-21 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…

Optimization and Control · Mathematics 2025-12-05 P. Jameson Graber , Kyle Rosengartner

Inverse game theory is utilized to infer the cost functions of all players based on game outcomes. However, existing inverse game theory methods do not consider the learner as an active participant in the game, which could significantly…

Computer Science and Game Theory · Computer Science 2025-10-20 Jianguo Chen , Jinlong Lei , Biqiang Mu , Yiguang Hong , Hongsheng Qi

Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, while minimizing a cost. The optimal transition rates are…

Systems and Control · Computer Science 2018-02-13 Leonardo Stella , Dario Bauso

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary…

Optimization and Control · Mathematics 2015-09-23 Diogo A. Gomes , Joana Mohr , Rafael R. Souza

We study a class of deterministic mean field games and related optimal control problems, with a finite time horizon and in which the state space is a network. An agent controls her velocity, and, when she occupies a vertex, she can either…

Optimization and Control · Mathematics 2025-11-25 Yves Achdou , Claudio Marchi , Nicoletta Tchou

We consider deterministic Mean Field Games (MFG) in all Euclidean space with a cost functional continuous with respect to the distribution of the agents and attaining its minima in a compact set. We first show that the static MFG with such…

Analysis of PDEs · Mathematics 2024-03-18 Martino Bardi , Hicham Kouhkouh

Financial markets and more generally macro-economic models involve a large number of individuals interacting through variables such as prices resulting from the aggregate behavior of all the agents. Mean field games have been introduced to…

Optimization and Control · Mathematics 2021-07-12 René Carmona , Mathieu Laurière

Mean field games (MFG) are dynamic games with infinitely many infinitesimal agents. In this context, we study the efficiency of Nash MFG equilibria: Namely, we compare the social cost of a MFG equilibrium with the minimal cost a global…

Optimization and Control · Mathematics 2018-02-20 Pierre Cardaliaguet , Catherine Rainer

We construct a semi-Lagrangian scheme for first-order, time-dependent, and non-local Mean Field Games. The convergence of the scheme to a weak solution of the system is analyzed by exploiting a key monotonicity property. To solve the…

Numerical Analysis · Mathematics 2026-05-12 Elisabetta Carlini , Valentina Coscetti

We consider deterministic mean field games in which the agents control their acceleration and are constrained to remain in a domain of R n. We study relaxed equilibria in the Lagrangian setting; they are described by a probability measure…

Analysis of PDEs · Mathematics 2021-11-04 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou