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In this paper, the existence of non-trivial time periodic solutions of first order mean field games is proved. It is assumed that there is a non-trivial periodic orbit contained in the Mather set. The whole system is autonomous with a…

Analysis of PDEs · Mathematics 2024-01-17 Panrui Ni

In this paper, we study the well-posedness (existence and uniqueness) of the Master Equation of Mean Field Games under invariance-type conditions, otherwise known as viability conditions for the controlled dynamics. The interior regularity…

Analysis of PDEs · Mathematics 2022-11-15 Antonios Zitridis

We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical…

Computer Science and Game Theory · Computer Science 2010-12-13 Sachin Adlakha , Ramesh Johari

We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…

Optimization and Control · Mathematics 2019-07-26 Jodi Dianetti , Giorgio Ferrari , Markus Fischer , Max Nendel

This note highlights a special class of mean field games in which the coefficients satisfy a convolution-type structural condition. A mean field game of this type with common noise is related to a certain mean field game without common…

Probability · Mathematics 2014-09-26 Daniel Lacker , Kevin Webster

In this paper, we consider a system of forward-backward stochastic differential equations (FBSDEs) with monotone functionals. We show the existence and uniqueness of such a system by the method of continuation similarly to Peng and Wu…

Probability · Mathematics 2018-08-07 Saran Ahuja , Weiluo Ren , Tzu-Wei Yang

The standard solution concept for stochastic games is Markov perfect equilibrium (MPE); however, its computation becomes intractable as the number of players increases. Instead, we consider mean field equilibrium (MFE) that has been…

Theoretical Economics · Economics 2020-06-05 Bar Light , Gabriel Weintraub

This paper develops a unified framework for proving the existence of solutions to stationary first-order mean-field games (MFGs) based on the theory of monotone operators in Banach spaces. We cast the coupled MFG system as a variational…

Analysis of PDEs · Mathematics 2026-03-17 Rita Ferreira , Diogo Gomes , Melih Ucer

This paper investigates a linear-quadratic mean field games problem with common noise, where the drift term and diffusion term of individual state equations are coupled with both the state, control, and mean field terms of the state, and we…

Optimization and Control · Mathematics 2025-08-12 Wenyu Cong , Jingtao Shi , Bingchang Wang

In the context of simple finite-state discrete time systems, we introduce a generalization of mean field game solution, called correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. Our notion of…

Optimization and Control · Mathematics 2021-07-12 Luciano Campi , Markus Fischer

In this paper, we address an instance of uniquely solvable mean-field game with a common noise whose corresponding counterpart without common noise has several equilibria. We study the selection problem for this mean-field game without…

Probability · Mathematics 2018-08-29 François Delarue , Rinel Foguen Tchuendom

It is well known that the monotonicity condition, either in Lasry-Lions sense or in displacement sense, is crucial for the global well-posedness of mean field game master equations, as well as for the uniqueness of mean field equilibria and…

Probability · Mathematics 2022-11-24 Chenchen Mou , Jianfeng Zhang

We establish the existence and uniqueness of a solution to the master equation for a mean field game of controls with absorption. The mean field game arises as a continuum limit of a dynamic game of exhaustible resources modeling Cournot…

Analysis of PDEs · Mathematics 2022-08-25 P. Jameson Graber , Ronnie Sircar

In this manuscript, we propose a structural condition on non-separable Hamiltonians, which we term displacement monotonicity condition, to study second order mean field games master equations. A rate of dissipation of a bilinear form is…

Analysis of PDEs · Mathematics 2022-04-04 Wilfrid Gangbo , Alpár R. Mészáros , Chenchen Mou , Jianfeng Zhang

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 formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on…

Optimization and Control · Mathematics 2023-10-10 Yuan Gao , Wuchen Li , Jian-Guo Liu

We introduce a mean field game for a family of filtering problems related to the classic sequential testing of the drift of a Brownian motion. To the best of our knowledge this work presents the first treatment of mean field filtering games…

Optimization and Control · Mathematics 2024-03-28 Steven Campbell , Yuchong Zhang

We study a stationary first--order mean field game on the $d$--dimensional torus. The system couples a Hamilton--Jacobi equation for the value function with a transport equation for the density of players. Our goal is to give a detailed and…

Functional Analysis · Mathematics 2025-12-11 Hikmatullo Ismatov

The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…

Optimization and Control · Mathematics 2019-03-19 Bruce Hajek , Michael Livesay

We study the convergence problem for mean field games with common noise and controlled volatility. We adopt the strategy recently put forth by Lauri\`ere and the second author, using the maximum principle to recast the convergence problem…

Probability · Mathematics 2023-10-20 Joe Jackson , Ludovic Tangpi