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Related papers: Linear Quadratic Graphon Field Games

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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

Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…

Optimization and Control · Mathematics 2022-04-20 Nian Liu , Lei Guo

Mean field games (MFGs) tractably model behavior in large agent populations. The literature on learning MFG equilibria typically focuses on finding Nash equilibria (NE), which assume perfectly rational agents and are hence implausible in…

Computer Science and Game Theory · Computer Science 2025-01-31 Yannick Eich , Christian Fabian , Kai Cui , Heinz Koeppl

Network Creation Games(NCGs) model the creation of decentralized communication networks like the Internet. In such games strategic agents corresponding to network nodes selfishly decide with whom to connect to optimize some objective…

Computer Science and Game Theory · Computer Science 2020-06-29 Hagen Echzell , Tobias Friedrich , Pascal Lenzner , Anna Melnichenko

This paper investigates mean field games and control on sparse networks. In the case of large expander graphs, the limit topologies are analyzed using the graphexon framework, which characterizes both dense network limits and sparse…

Optimization and Control · Mathematics 2026-04-16 Tao Zhang , Peter E. Caines

This paper studies the limits of empirical means of open-loop Nash equilibria of linear-quadratic stochastic differential games as the number of players goes to infinity, when the corresponding mean field game is of potential type and may…

Probability · Mathematics 2026-02-27 Alekos Cecchin , Jodi Dianetti

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 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

Mean Field Games (MFG) have been introduced to tackle games with a large number of competing players. Considering the limit when the number of players is infinite, Nash equilibria are studied by considering the interaction of a typical…

Optimization and Control · Mathematics 2021-06-14 Mathieu Lauriere

Motivated by recent works addressing adversarial attacks on deep reinforcement learning, a deception attack on linear quadratic Gaussian control is studied in this paper. In the considered attack model, the adversary can manipulate the…

Systems and Control · Electrical Eng. & Systems 2020-09-11 Zuxing Li , György Dán , Dong Liu

Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon…

Signal Processing · Electrical Eng. & Systems 2023-12-18 Luana Ruiz , Luiz F. O. Chamon , Alejandro Ribeiro

Security games model strategic interactions in adversarial real-world applications. Such applications often involve extremely large but highly structured strategy sets (e.g., selecting a distribution over all patrol routes in a given…

Computer Science and Game Theory · Computer Science 2025-04-22 Jakub Černý , Chun Kai Ling , Christian Kroer , Garud Iyengar

Mean field game theory has been developed largely following two routes. One of them, called the direct approach, starts by solving a large-scale game and next derives a set of limiting equations as the population size tends to infinity. The…

Optimization and Control · Mathematics 2019-05-23 Minyi Huang , Mengjie Zhou

Graph neural networks (GNNs) are learning architectures that rely on knowledge of the graph structure to generate meaningful representations of large-scale network data. GNN stability is thus important as in real-world scenarios there are…

Machine Learning · Computer Science 2021-04-27 Luana Ruiz , Zhiyang Wang , Alejandro Ribeiro

For any two-by-two game $\G$, we define a new two-player game $\G^Q$. The definition is motivated by a vision of players in game $\G$ communicating via quantum technology according to a certain standard protocol originally introduced by…

Optimization and Control · Mathematics 2011-10-07 Steven E. Landsburg

This paper is concerned with a new class of mean-field games which involve a finite number of agents. Necessary and sufficient conditions are obtained for the existence of the decentralized open-loop Nash equilibrium in terms of…

Optimization and Control · Mathematics 2022-06-14 Bing-Chang Wang , Huanshui Zhang , Minyue Fu , Yong Liang

Motivated by mean-field games (MFG) with common noise on the one hand and pathwise stochastic control theory on the other, we formulate here a linear-quadratic (LQ) MFG with rough common noise, along with a satisfactory well-posedness…

Probability · Mathematics 2026-04-14 Peter K. Friz , Ioannis Gasteratos , Ulrich Horst , Stefanos Theodorakopoulos

Mean field games were introduced independently by J-M. Lasry and P-L. Lions, and by M. Huang, R.P. Malham\'e and P. E. Caines, in order to bring a new approach to optimization problems with a large number of interacting agents. The…

Physics and Society · Physics 2018-08-13 Denis Ullmo , Igor Swiecicki , Thierry Gobron

In this paper, we study graphon mean field games using a system of forward-backward stochastic differential equations. We establish the existence and uniqueness of solutions under two different assumptions and prove the stability with…

Probability · Mathematics 2022-02-17 Erhan Bayraktar , Ruoyu Wu , Xin Zhang

In a graphical game agents play with their neighbors on a graph to achieve an appropriate state of equilibrium. Here relevant problems are characterizing the equilibrium set and discovering efficient algorithms to find such an equilibrium…

Statistical Mechanics · Physics 2011-09-06 A. Ramezanpour , J. Realpe-Gomez , R. Zecchina