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A novel framework is presented that combines Mean Field Game (MFG) theory and Hybrid Optimal Control (HOC) theory to obtain a unique $\epsilon$-Nash equilibrium for a non-cooperative game with switching and stopping times. We consider the…

Systems and Control · Computer Science 2022-01-11 Dena Firoozi , Ali Pakniyat , Peter E. Caines

We introduce a mean field model for optimal holding of a representative agent of her peers as a natural expected scaling limit from the corresponding $N-$agent model. The induced mean field dynamics appear naturally in a form which is not…

Optimization and Control · Mathematics 2022-04-05 Mao Fabrice Djete , Nizar Touzi

In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of deterministic mean field games and master equations, where the interaction of the agents happens…

Analysis of PDEs · Mathematics 2024-03-25 P. Jameson Graber , Alpár R. Mészáros

We are interested in the study of stochastic games for which each player faces an optimal stopping problem. In our setting, the players may interact through the criterion to optimise as well as through their dynamics. After briefly…

Probability · Mathematics 2025-09-03 Dylan Possamaï , Mehdi Talbi

In many stochastic games stemming from financial models, the environment evolves with latent factors and there may be common noise across agents' states. Two classic examples are: (i) multi-agent trading on electronic exchanges, and (ii)…

Optimization and Control · Mathematics 2019-07-24 Dena Firoozi , Peter E. Caines , Sebastian Jaimungal

This paper studies a type of rank-based mean field game in which competing agents strategically switch among multiple effort regimes. We propose an entropy regularized auxiliary problem where the switching decisions are randomized to the…

Optimization and Control · Mathematics 2026-05-29 Zongxia Liang , Shu Wang , Xiang Yu

Mean field games (MFGs) model equilibria in games with a continuum of weakly interacting players as limiting systems of symmetric $n$-player games. We consider the finite-state, infinite-horizon problem with ergodic cost. Assuming Markovian…

Optimization and Control · Mathematics 2025-03-25 Asaf Cohen , Ethan Zell

In this work, we present an application of the probabilistic weak formulation of mean field games (MFG) for modeling liquidity pools in a constant product automated market maker (AMM) protocol in the context of decentralized finance. Our…

Optimization and Control · Mathematics 2026-04-14 Agustín Muñoz González , Juan I. Sequeira , Rafael Orive Illera

In this paper we study a type of games regularized by the relative entropy, where the players' strategies are coupled through a random environment variable. Besides the existence and the uniqueness of equilibria of such games, we prove that…

Computer Science and Game Theory · Computer Science 2020-04-24 Giovanni Conforti , Anna Kazeykina , Zhenjie Ren

Stochastic games provide a framework for interactions among multiple agents and enable a myriad of applications. In these games, agents decide on actions simultaneously, the state of every agent moves to the next state, and each agent…

Machine Learning · Computer Science 2019-10-10 Mridul Agarwal , Vaneet Aggarwal , Arnob Ghosh , Nilay Tiwari

Mean Field Control Games (MFCGs) provide a powerful theoretical framework for analyzing systems of infinitely many interacting agents, blending elements from Mean Field Games (MFGs) and Mean Field Control (MFC). However, solving the coupled…

Machine Learning · Computer Science 2025-01-03 Nianli Peng , Yilin Wang

We study discrete-time mean-field Markov games with infinite numbers of agents where each agent aims to minimize its ergodic cost. We consider the setting where the agents have identical linear state transitions and quadratic cost…

Optimization and Control · Mathematics 2019-10-17 Zuyue Fu , Zhuoran Yang , Yongxin Chen , Zhaoran Wang

We study the uniqueness of solutions to systems of PDEs arising in Mean Field Games with several populations of agents and Neumann boundary conditions. The main assumption requires the smallness of some data, e.g., the length of the time…

Analysis of PDEs · Mathematics 2017-09-08 Martino Bardi , Marco Cirant

Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and…

Computer Science and Game Theory · Computer Science 2023-12-19 Kai Cui , Gökçe Dayanıklı , Mathieu Laurière , Matthieu Geist , Olivier Pietquin , Heinz Koeppl

In two-player zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have…

Optimization and Control · Mathematics 2019-07-30 Yagiz Savas , Mohamadreza Ahmadi , Takashi Tanaka , Ufuk Topcu

We formulate the MFG limit for $N$ interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We prove that any its (regular enough) solution…

Probability · Mathematics 2022-04-21 Vassili Kolokoltsov , Marianna Troeva

In this paper, we propose and study a mean field game model with multiple populations of minor players and multiple major players, motivated by applications to the regulation of carbon emissions. Each population of minor players represent a…

Optimization and Control · Mathematics 2023-09-29 Gokce Dayanikli , Mathieu Lauriere

This paper studies the equilibrium consumption under external habit formation in a large population of agents. We first formulate problems under two types of conventional habit formation preferences, namely linear and multiplicative…

Mathematical Finance · Quantitative Finance 2024-03-11 Lijun Bo , Shihua Wang , Xiang Yu

In this paper, we study the infinite-time mean field games with discounting, establishing an equilibrium where individual optimal strategies collectively regenerate the mean-field distribution. To solve this problem, we partition all agents…

Optimization and Control · Mathematics 2026-03-17 Yongsheng Song , Zeyu Yang

We study a static game played by a finite number of agents, in which agents are assigned independent and identically distributed random types and each agent minimizes its objective function by choosing from a set of admissible actions that…

Probability · Mathematics 2017-02-08 Daniel Lacker , Kavita Ramanan