English
Related papers

Related papers: Linear Mean-Field Games with Discounted Cost

200 papers

We consider N-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to {-1,1}. If there is uniqueness of mean field game solutions, e.g. under monotonicity assumptions, then the…

Optimization and Control · Mathematics 2019-02-06 Alekos Cecchin , Paolo Dai Pra , Markus Fischer , Guglielmo Pelino

The aim of this paper is to study first order Mean field games subject to a linear controlled dynamics on $\mathbb R^{d}$. For this kind of problems, we define Nash equilibria (called Mean Field Games equilibria), as Borel probability…

Optimization and Control · Mathematics 2019-12-11 Piermarco Cannarsa , Cristian Mendico

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

Synthesis of finite-state controllers from high-level specifications in multi-agent systems can be reduced to solving multi-player concurrent games over finite graphs. The complexity of solving such games with qualitative objectives for…

Computer Science and Game Theory · Computer Science 2018-09-28 Shaull Almagor , Rajeev Alur , Suguman Bansal

We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games…

Optimization and Control · Mathematics 2025-09-23 Haoyang Cao , Jodi Dianetti , Giorgio Ferrari

Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…

Probability · Mathematics 2015-04-09 Rene Carmona , Daniel Lacker

This paper is concerned with a new class of mean-field games which involve a finite number of agents. Necessary and sufficient conditions are obtained for the existence of the decentralized open-loop Nash equilibrium in terms of…

Optimization and Control · Mathematics 2022-06-14 Bing-Chang Wang , Huanshui Zhang , Minyue Fu , Yong Liang

We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…

Probability · Mathematics 2014-09-26 Rene Carmona , Xiuneng Zhu

We formulate and solve a multi-player stochastic differential game between financial agents who seek to cost-efficiently liquidate their position in a risky asset in the presence of jointly aggregated transient price impact, along with…

Trading and Market Microstructure · Quantitative Finance 2023-03-24 Eyal Neuman , Moritz Voß

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 consider a general class of finite-player stochastic games with mean-field interaction, in which the linear-quadratic cost functional includes linear operators acting on controls in $L^2$. We propose a novel approach for deriving the…

Optimization and Control · Mathematics 2024-02-16 Eduardo Abi Jaber , Eyal Neuman , Moritz Voß

This article considers a mean field game model inspired by crowd motion models in which agents aim at reaching a given target set and wish to minimize a cost consisting of an individual running cost, an individual cost depending on the…

Optimization and Control · Mathematics 2026-02-20 Guilherme Mazanti , Laurent Pfeiffer , Saeed Sadeghi Arjmand

Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this…

Optimization and Control · Mathematics 2019-10-31 Martin Frank , Michael Herty , Torsten Trimborn

This paper investigates an indefinite linear-quadratic partially observed mean-field game with common noise, incorporating both state-average and control-average effects. In our model, each agent's state is observed through both individual…

Optimization and Control · Mathematics 2025-08-05 Tian Chen , Tianyang Nie , Zhen Wu

Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading…

Mathematical Finance · Quantitative Finance 2019-12-13 Philippe Casgrain , Sebastian Jaimungal

Conventional Mean-field games/control study the behavior of a large number of rational agents moving in the Euclidean spaces. In this work, we explore the mean-field games on Riemannian manifolds. We formulate the mean-field game Nash…

Optimization and Control · Mathematics 2023-04-26 Jiajia Yu , Rongjie Lai , Wuchen Li , Stanley Osher

Motivated by models of epidemic control in large populations, we consider a Stackelberg mean field game model between a principal and a mean field of agents evolving on a finite state space. The agents play a non-cooperative game in which…

Optimization and Control · Mathematics 2021-05-26 Alexander Aurell , Rene Carmona , Gokce Dayanikli , Mathieu Lauriere

We study stochastic mean-field games among finite number of teams with large finite as well as infinite number of decision makers. For this class of games within static and dynamic settings, we establish the existence of a Nash equilibrium,…

Optimization and Control · Mathematics 2022-11-11 Sina Sanjari , Naci Saldi , Serdar Yüksel

Recently, the paper [12] introduces a derivative-free consensus-based particle method that finds the Nash equilibrium of non-convex multiplayer games, where it proves the global exponential convergence in the sense of mean-field law. This…

Optimization and Control · Mathematics 2025-05-21 Hui Huang , Jethro Warnett

This paper studies the n-player game and the mean field game under the CRRA relative performance on terminal wealth, in which the interaction occurs by peer competition. In the model with n agents, the price dynamics of underlying risky…

Mathematical Finance · Quantitative Finance 2023-02-10 Lijun Bo , Shihua Wang , Xiang Yu