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Equilibria of realistic multiplayer games constitute a key solution concept both in practical applications, such as online advertising auctions and electricity markets, and in analytical frameworks used to study strategic voting in…

Computer Science and Game Theory · Computer Science 2025-11-18 Jakub Černý , Shuvomoy Das Gupta , Christian Kroer

Mean field games with a major player were introduced in (Huang, 2010) within a linear-quadratic (LQ) modeling framework. Due to the rich structure of major-minor player models, the past ten years have seen significant research efforts for…

Optimization and Control · Mathematics 2021-06-15 Minyi Huang

Motivated by the fact that in many game-theoretic settings, the game analyzed is only an approximation to the game being played, in this work we analyze equilibrium computation for the broad and natural class of bimatrix games that are…

Computer Science and Game Theory · Computer Science 2012-03-14 Maria-Florina Balcan , Mark Braverman

A new class of projected dynamical systems of third order is investigated for quasi (parametric) variational inequalities in which the convex set in the classical variational inequality also depends upon the solution explicitly or…

Optimization and Control · Mathematics 2025-01-10 Oday Hazaimah

This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…

Machine Learning · Computer Science 2023-01-05 Xin Guo , Anran Hu , Renyuan Xu , Junzi Zhang

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

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

This work introduces a new general approach for the numerical analysis of stable equilibria to second order mean field games systems in cases where the uniqueness of solutions may fail. For the sake of simplicity, we focus on a simple…

Analysis of PDEs · Mathematics 2024-10-30 Jules Berry , Olivier Ley , Francisco J Silva

We study the existence and computation of Nash equilibria in concave games where the players' admissible strategies are subject to shared coupling constraints. Under playerwise concavity of constraints, we prove existence of Nash…

Computer Science and Game Theory · Computer Science 2026-02-09 Philip Jordan , Maryam Kamgarpour

In this paper, we provide a sufficient condition of the energy equality for the incompressible Navier-Stokes equations in bounded domains.

Analysis of PDEs · Mathematics 2018-02-22 Cheng Yu

Mean field Game (MFG) Partial Differential Inclusions (PDI) are generalizations of the system of Partial Differential Equations (PDE) of Lasry and Lions to situations where players in the game may have possibly nonunique optimal controls,…

Optimization and Control · Mathematics 2025-09-15 Yohance A. P. Osborne , Iain Smears

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 discuss a natural game of competition and solve the corresponding mean field game with \emph{common noise} when agents' rewards are \emph{rank dependent}. We use this solution to provide an approximate Nash equilibrium for the finite…

Probability · Mathematics 2016-10-18 Erhan Bayraktar , Yuchong Zhang

We study a family of mean field games arising in modeling the behavior of strategic economic agents which move across space maximizing their utility from consumption and have the possibility to accumulate resources for production (such as…

Analysis of PDEs · Mathematics 2026-01-22 Daria Ghilli , Fausto Gozzi , Giovanni Zanco

We study a toy model of linear-quadratic mean field game with delay. We "lift" the delayed dynamic into an infinite dimensional space, and recast the mean field game system which is made of a forward Kolmogorov equation and a backward…

Probability · Mathematics 2018-08-21 Jean-Pierre Fouque , Zhaoyu Zhang

In this paper we investigate Nash equilibrium payoffs for two-player nonzero-sum stochastic differential games whose cost functionals are defined by a system of coupled backward stochastic differential equations. We obtain an existence…

Probability · Mathematics 2014-01-21 Qian Lin

To find the possible equilibrium states of forest ecosystems one are suggested to use the theory of differential games. At within the 4-tier model of mosaic forest communities it established the existence of the Nash equilibrium states in…

Other Quantitative Biology · Quantitative Biology 2016-11-01 Alexander K. Guts , Ludmila A. Volodchenkova

We study the mean field games equations, consisting of the coupled Kolmogorov-Fokker-Planck and Hamilton-Jacobi-Bellman equations. The equations are complemented by initial and terminal conditions. It is shown that with some specific choice…

Analysis of PDEs · Mathematics 2019-11-22 Sergey I. Nikulin , Olga S. Rozanova

We consider second-order ergodic Mean-Field Games systems in the whole space $\mathbb{R}^N$ with coercive potential and aggregating nonlocal coupling, defined in terms of a Riesz interaction kernel. These MFG systems describe Nash…

Analysis of PDEs · Mathematics 2023-05-01 Chiara Bernardini , Annalisa Cesaroni

This paper studies the mean field game (MFG) problem arising from a large population competition in fund management, featuring a new type of relative performance via the benchmark tracking. In the $n$-player model, each agent aims to…

Optimization and Control · Mathematics 2026-04-16 Lijun Bo , Yijie Huang , Xiang Yu