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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

The purpose of this paper is to provide a complete probabilistic analysis of a large class of stochastic differential games for which the interaction between the players is of mean-field type. We implement the Mean-Field Games strategy…

Probability · Mathematics 2012-10-23 Rene Carmona , Francois Delarue

We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest…

Optimization and Control · Mathematics 2014-02-28 Yasin Abbasi-Yadkori , Peter L. Bartlett , Alan Malek

Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics…

Optimization and Control · Mathematics 2020-07-23 Lisang Ding , Wuchen Li , Stanley Osher , Wotao Yin

We propose a mean field game (MFG) framework to model the evolution of renewable energy production in competitive electricity markets. Producers interact through the spot price while optimising their profits under production, installation,…

Optimization and Control · Mathematics 2026-03-25 Luciano Campi , Zhuoshu Wu

Motivated by continuous-time optimal inventory management, we study a class of stationary mean-field control problems with singular controls. The dynamics are modeled by a mean-reverting Ornstein-Uhlenbeck process, and the performance…

Optimization and Control · Mathematics 2026-02-02 Federico Cannerozzi

In a game theoretic framework, we study energy markets with a continuum of homogenous producers who produce energy from an exhaustible resource such as oil. Each producer simultaneously optimizes production rate that drives her revenues, as…

Economics · Quantitative Finance 2017-10-17 Michael Ludkovski , Xuwei Yang

The framework of Mean-field Games (MFGs) is used for modelling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative…

Optimization and Control · Mathematics 2024-07-29 Piyush Grover , Mandy Huo

In this paper, we investigate the mean field games with $K$ classes of agents who are weakly coupled via the empirical measure. The underlying dynamics of the representative agents is assumed to be a controlled nonlinear Markov process…

Probability · Mathematics 2012-04-09 Vassili N. Kolokoltsov , Jiajie Li , Wei Yang

In this paper, we use mean field games (MFGs) to investigate approximations of $N$-player games with uniformly symmetrically continuous heterogeneous closed-loop actions. To incorporate agents' risk aversion (beyond the classical expected…

Optimization and Control · Mathematics 2024-09-26 Ziteng Cheng , Sebastian Jaimungal

This paper considers the discounted criterion of nonzero-sum decentralized stochastic games with prospect players. The state and action spaces are finite. The state transition probability is nonstationary. Each player independently controls…

Optimization and Control · Mathematics 2024-05-16 Yiting Wu , Junyu Zhang

Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players…

Systems and Control · Computer Science 2018-06-06 Naci Saldi , Tamer Basar , Maxim Raginsky

We consider a mean field game describing the limit of a stochastic differential game of $N$-players whose state dynamics are subject to idiosyncratic and common noise and that can be absorbed when they hit a prescribed region of the state…

Probability · Mathematics 2022-05-25 Matteo Burzoni , Luciano Campi

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…

Optimization and Control · Mathematics 2008-06-17 Parikshit Shah , Pablo A. Parrilo

We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank…

Optimization and Control · Mathematics 2018-11-02 Erhan Bayraktar , Jakša Cvitanić , Yuchong Zhang

In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of…

Optimization and Control · Mathematics 2017-11-07 Piermarco Cannarsa , Rossana Capuani

We analyze a mean field tournament: a mean field game in which the agents receive rewards according to the ranking of the terminal value of their projects and are subject to cost of effort. Using Schr\"{o}dinger bridges we are able to…

Optimization and Control · Mathematics 2020-06-23 Erhan Bayraktar , Yuchong Zhang

We present a new notion of solution for mean field games master equations. This notion allows us to work with solutions which are merely continuous. We prove first results of uniqueness and stability for such solutions. It turns out that…

Analysis of PDEs · Mathematics 2020-07-24 Charles Bertucci

We introduce a mean-field term to an evolutionary spatial game model. Namely, we consider the game of Nowak and May, based on the Prisoner's dilemma, and augment the game rules by a self-consistent mean-field term. This way, an agent…

Statistical Mechanics · Physics 2021-09-29 Dmitriy Antonov , Evgeni Burovski , Lev Shchur

We consider Mean Field Games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution…

Analysis of PDEs · Mathematics 2020-09-28 Pierre Cardaliaguet , Panagiotis Souganidis