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We study a class of linear-quadratic stochastic differential games in which each player interacts directly only with its nearest neighbors in a given graph. We find a semi-explicit Markovian equilibrium for any transitive graph, in terms of…

Probability · Mathematics 2021-09-27 Daniel Lacker , Agathe Soret

Consider an interacting particle system indexed by the vertices of a (possibly random) locally finite graph whose vertices and edges are equipped with marks representing parameters of the model such as the environment and initial…

Probability · Mathematics 2024-07-31 Ankan Ganguly , Kavita Ramanan

This paper investigates the limit behavior of Markov Decision Processes (MDPs) made of independent particles evolving in a common environment, when the number of particles goes to infinity. In the finite horizon case or with a discounted…

Probability · Mathematics 2009-06-10 Nicolas Gast , Bruno Gaujal

Recent advances at the intersection of dense large graph limits and mean field games have begun to enable the scalable analysis of a broad class of dynamical sequential games with large numbers of agents. So far, results have been largely…

Computer Science and Game Theory · Computer Science 2022-02-21 Kai Cui , Heinz Koeppl

We consider finite horizon stochastic mean field games in which the state space is a network. They are described by a system coupling a backward in time Hamilton-Jacobi-Bellman equation and a forward in time Fokker-Planck equation. The…

Analysis of PDEs · Mathematics 2019-03-08 Yves Achdou , Manh-Khang Dao , Olivier Ley , Nicoletta Tchou

In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…

Probability · Mathematics 2022-12-06 Maxime Hauray , Etienne Pardoux , Yen V. Vuong

We study a general class of interacting particle systems over a countable state space $V$ where on each site $x \in V$ the particle mass $\eta(x) \geq 0$ follows a stochastic differential equation. We construct the corresponding Markovian…

Probability · Mathematics 2023-08-16 Viktor Bezborodov , Luca Di Persio , Martin Friesen , Peter Kuchling

This paper is devoted to finite horizon deterministic mean field games in which the state space is a network. The agents control their velocity, and when they occupy a vertex, they can enter into any incident edge. The running and terminal…

Optimization and Control · Mathematics 2023-11-21 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

We explore a mechanism of decision-making in Mean Field Games with myopic players. At each instant, agents set a strategy which optimizes their expected future cost by assuming their environment as immutable. As the system evolves, the…

Optimization and Control · Mathematics 2018-02-05 Charafeddine Mouzouni

We study two interacting particle systems, both modeled as a system of $N$ stochastic differential equations driven by Brownian motions with singular kernels and moderate interaction. We show a quantitative result where the convergence rate…

Probability · Mathematics 2025-01-22 Josué Knorst , Christian Olivera , Alexandre B. de Souza

We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them…

Probability · Mathematics 2012-10-02 Ioannis Karatzas , Soumik Pal , Mykhaylo Shkolnikov

Strategic network formation arises where agents receive benefit from connections to other agents, but also incur costs for forming links. We consider a new network formation game that incorporates an adversarial attack, as well as…

Computer Science and Game Theory · Computer Science 2016-11-10 Sanjeev Goyal , Shahin Jabbari , Michael Kearns , Sanjeev Khanna , Jamie Morgenstern

We study the mean field approximation of a recent model of cascades on networks relevant to the investigation of systemic risk control in financial networks. In the model, the hypothesis of a trend reinforcement in the stochastic process…

Physics and Society · Physics 2007-11-13 Jan Lorenz , Stefano Battiston

In this work, we consider one-dimensional particles interacting in mean-field type through a bounded kernel. In addition, when particles hit some barrier (say zero), they are removed from the system. This absorption of particles is…

Probability · Mathematics 2026-04-07 Gaoyue Guo , Maxime Latypov , Milica Tomasevic

We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…

Probability · Mathematics 2025-06-09 Pascal Bianchi , Walid Hachem , Victor Priser

We study the uniqueness of solutions to systems of PDEs arising in Mean Field Games with several populations of agents and Neumann boundary conditions. The main assumption requires the smallness of some data, e.g., the length of the time…

Analysis of PDEs · Mathematics 2017-09-08 Martino Bardi , Marco Cirant

A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition…

Probability · Mathematics 2011-06-17 Amarjit Budhiraja , Pierre Del Moral , Sylvain Rubenthaler

Time-limited states characterise many dynamical processes on networks: disease infected individuals recover after some time, people forget news spreading on social networks, or passengers may not wait forever for a connection. These…

Physics and Society · Physics 2023-06-13 Arash Badie-Modiri , Márton Karsai , Mikko Kivelä

In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on…

Chaotic Dynamics · Physics 2015-09-30 Gilles Wainrib , Mathieu Galtier

Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle…

Probability · Mathematics 2024-01-02 Kavita Ramanan