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Related papers: Mean Field Games and Nonlinear Markov Processes

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The goal of the paper is to introduce a formulation of the mean field game with major and minor players as a fixed point on a space of controls. This approach emphasizes naturally the role played by McKean-Vlasov dynamics in some of the…

Probability · Mathematics 2016-10-19 Rene Carmona , Peiqi Wang

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

In single-agent Markov decision processes, an agent can optimize its policy based on the interaction with environment. In multi-player Markov games (MGs), however, the interaction is non-stationary due to the behaviors of other players, so…

Computer Science and Game Theory · Computer Science 2021-10-19 Yuanheng Zhu , Dongbin Zhao , Mengchen Zhao , Dong Li

We establish a functional weak law of large numbers for observable macroscopic state variables of interacting particle systems (e.g., voter and contact processes) over fast time-varying sparse random networks of interactions. We show that,…

Probability · Mathematics 2017-03-01 Augusto Almeida Santos , Soummya Kar , José M. F. Moura , João Xavier

We study a general class of entropy-regularized multi-variate LQG mean field games (MFGs) in continuous time with $K$ distinct sub-population of agents. We extend the notion of actions to action distributions (exploratory actions), and…

Optimization and Control · Mathematics 2021-12-01 Dena Firoozi , Sebastian Jaimungal

This paper studies approximate solutions to large-scale linear quadratic stochastic games with homogeneous nodal dynamics parameters and heterogeneous network couplings within the graphon mean field game framework in [2]-[4]. A graphon…

Systems and Control · Electrical Eng. & Systems 2021-10-22 Shuang Gao , Peter E. Caines , Minyi Huang

In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…

Optimization and Control · Mathematics 2025-12-05 P. Jameson Graber , Kyle Rosengartner

This paper deals with N-person nonzero-sum discrete-time Markov games under a probability criterion, in which the transition probabilities and reward functions are allowed to vary with time. Differing from the existing works on the expected…

Probability · Mathematics 2025-05-16 Xin Guo , Xin Wen

We consider N-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to {-1,1}. If there is uniqueness of mean field game solutions, e.g. under monotonicity assumptions, then the…

Optimization and Control · Mathematics 2019-02-06 Alekos Cecchin , Paolo Dai Pra , Markus Fischer , Guglielmo Pelino

This paper considers a class of reinforcement-learning that belongs to the family of Learning Automata and provides a stochastic-stability analysis in strategic-form games. For this class of dynamics, convergence to pure Nash equilibria has…

Computer Science and Game Theory · Computer Science 2017-02-28 Georgios C. Chasparis

This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…

Probability · Mathematics 2022-03-24 Mathieu Laurière , Ludovic Tangpi

We consider a symmetric $n$-player nonzero-sum stochastic differential game with controlled jumps and mean-field type interaction among the players. Each player minimizes some expected cost by affecting the drift as well as the jump part of…

Probability · Mathematics 2018-05-14 Chiara Benazzoli , Luciano Campi , Luca Di Persio

Network games provide a natural machinery to compactly represent strategic interactions among agents whose payoffs exhibit sparsity in their dependence on the actions of others. Besides encoding interaction sparsity, however, real networks…

Computational Engineering, Finance, and Science · Computer Science 2021-01-22 Kun Jin , Yevgeniy Vorobeychik , Mingyan Liu

We investigate mean-field games (MFG) in which agents can actively control their speed of access to information. Specifically, the agents can dynamically decide to obtain observations with reduced delay by accepting higher observation…

Optimization and Control · Mathematics 2025-06-03 Dirk Becherer , Christoph Reisinger , Jonathan Tam

The paper is concerned with the study of a control system consisting of one major agent and many identical minor agents in the limit case when the number of agents tends to infinity. To study the limiting system we use the mean field…

Optimization and Control · Mathematics 2022-12-13 Yurii Averboukh

In this article we consider zero and non-zero sum risk-sensitive average criterion games for semi-Markov processes with a finite state space. For the zero-sum case, under suitable assumptions we show that the game has a value. We also…

Optimization and Control · Mathematics 2021-06-10 Arnab Bhabak , Subhamay Saha

This paper studies the n-player game and the mean field game under the CRRA relative performance on terminal wealth, in which the interaction occurs by peer competition. In the model with n agents, the price dynamics of underlying risky…

Mathematical Finance · Quantitative Finance 2023-02-10 Lijun Bo , Shihua Wang , Xiang Yu

We consider $N$-player games, in continuous time, finite state space and finite time horizon, on a geometrical structure possessing a macroscopic limit in a suitable sense. This geometrical structure breaks the permutation invariance…

Optimization and Control · Mathematics 2024-10-07 Francesca Albertini , Paolo Dai Pra

A mean field type differential game is a mathematical model of a large system of identical agents under mean-field interaction controlled by two players with opposite purposes. We study the case when the dynamics of each agent is given by…

Optimization and Control · Mathematics 2018-12-14 Yurii Averboukh

This paper is devoted to a class of finite horizon deterministic mean field games with Grushin type dynamics, state constraints and nonlocal coupling. First, we consider the optimal control problem that each agent aims to solve when the…

Optimization and Control · Mathematics 2026-02-16 Alessandra Cutrì , Paola Mannucci , Claudio Marchi , Nicoletta Tchou