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Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent…

Analysis of PDEs · Mathematics 2019-07-26 Diogo Gomes , Laurent Lafleche , Levon Nurbekyan

Mean-field games (MFG) were introduced to efficiently analyze approximate Nash equilibria in large population settings. In this work, we consider entropy-regularized mean-field games with a finite state-action space in a discrete time…

Computer Science and Game Theory · Computer Science 2022-07-26 Yue Guan , Mi Zhou , Ali Pakniyat , Panagiotis Tsiotras

We consider the basic problem of approximating Nash equilibria in noncooperative games. For monotone games, we design continuous time flows which converge in an averaged sense to Nash equilibria. We also study mean field equilibria, which…

Functional Analysis · Mathematics 2022-03-25 Ryan Hynd

In this paper, zero-sum mean-field type games (ZSMFTG) with linear dynamics and quadratic cost are studied under infinite-horizon discounted utility function. ZSMFTG are a class of games in which two decision makers whose utilities sum to…

Optimization and Control · Mathematics 2020-09-02 René Carmona , Kenza Hamidouche , Mathieu Laurière , Zongjun Tan

Mean field games (MFG) and mean field control problems (MFC) are frameworks to study Nash equilibria or social optima in games with a continuum of agents. These problems can be used to approximate competitive or cooperative games with a…

Optimization and Control · Mathematics 2021-06-28 Andrea Angiuli , Jean-Pierre Fouque , Mathieu Lauriere

Mean-field games (MFG) have become significant tools for solving large-scale multi-agent reinforcement learning problems under symmetry. However, the assumption of exact symmetry limits the applicability of MFGs, as real-world scenarios…

Computer Science and Game Theory · Computer Science 2024-08-28 Batuhan Yardim , Niao He

We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it as $n\to\infty$. However, both the finite and…

Optimization and Control · Mathematics 2019-05-30 Marcel Nutz , Jaime San Martin , Xiaowei Tan

This paper continues the study of the mean field game (MFG) convergence problem: In what sense do the Nash equilibria of $n$-player stochastic differential games converge to the mean field game as $n\rightarrow\infty$? Previous work on this…

Probability · Mathematics 2018-08-09 Daniel Lacker

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

We provide an in-depth study of Nash equilibria in multi-objective normal form games (MONFGs), i.e., normal form games with vectorial payoffs. Taking a utility-based approach, we assume that each player's utility can be modelled with a…

Computer Science and Game Theory · Computer Science 2022-07-19 Willem Röpke , Diederik M. Roijers , Ann Nowé , Roxana Rădulescu

This paper introduces a framework of Constrained Mean-Field Games (CMFGs), where each agent solves a constrained Markov decision process (CMDP). This formulation captures scenarios in which agents' strategies are subject to feasibility,…

Optimization and Control · Mathematics 2025-10-15 Anran Hu , Zijiu Lyu

In stochastic dynamic games, when the number of players is sufficiently large and the interactions between agents depend on empirical state distribution, one way to approximate the original game is to introduce infinite-population limit of…

Optimization and Control · Mathematics 2019-08-26 Naci Saldi

Mean field game equilibria are predicated on the assumption of immediate pairwise interactions within a population of homogeneous agents with asymptotically vanishing influence as population size increases. However, in many real-world…

Systems and Control · Electrical Eng. & Systems 2026-05-20 Farid Rajabali , Roland Malhame , Sadegh Bolouki

We consider mean field games with ergodic cost in the framework of a general discrete time controlled Markov processes. The state space of the processes is given by a general $\sigma$-compact Polish space. Under certain conditions, we show…

Probability · Mathematics 2015-11-02 Anup Biswas

We consider learning approximate Nash equilibria for discrete-time mean-field games with nonlinear stochastic state dynamics subject to both average and discounted costs. To this end, we introduce a mean-field equilibrium (MFE) operator,…

Systems and Control · Electrical Eng. & Systems 2022-11-11 Berkay Anahtarcı , Can Deha Karıksız , Naci Saldi

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

The partially observed major minor LQG and nonlinear mean field game (PO MM LQG MFG) systems where it is assumed the major agent's state is partially observed by each minor agent, and the major agent completely observes its own state have…

Optimization and Control · Mathematics 2020-09-11 Dena Firoozi , Peter E. Caines

Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout…

Optimization and Control · Mathematics 2019-12-30 Julien Claisse , Zhenjie Ren , Xiaolu Tan

Subject to reasonable conditions, in large population stochastic dynamics games, where the agents are coupled by the system's mean field (i.e. the state distribution of the generic agent) through their nonlinear dynamics and their nonlinear…

Optimization and Control · Mathematics 2019-05-28 Nevroz Sen , Peter E. Caines

In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. The state space of a generic agent is a compact Borel space. At every time, each agent is randomly…

Systems and Control · Electrical Eng. & Systems 2023-01-18 Naci Saldi