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Sensitivity of MFG SEIR-HCD Epidemiological Model
AbstractThe work is devoted to the global sensitivity analysis of the ‘‘mean field’’ epidemiological model based on SEIR-HCD population clustering....
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A singular perturbation problem for mean field games of acceleration: application to mean field games of control
The singular perturbation of mean field game systems arising from minimization problems with control of acceleration is addressed, that is, we...
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On some mean field games and master equations through the lens of conservation laws
In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of...
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Discrete potential mean field games: duality and numerical resolution
We propose and investigate a general class of discrete time and finite state space mean field game (MFG) problems with potential structure. Our model...
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Generic Properties of First-Order Mean Field Games
We consider a class of deterministic mean field games, where the state associated with each player evolves according to an ODE which is linear...
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Unified reinforcement Q-learning for mean field game and control problems
We present a Reinforcement Learning (RL) algorithm to solve infinite horizon asymptotic Mean Field Game (MFG) and Mean Field Control (MFC) problems....
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A System of Hamilton-Jacobi Equations Characterizing Geodesic Centroidal Tessellations
We introduce a class of systems of Hamilton-Jacobi equations characterizing geodesic centroidal tessellations, i.e., tessellations of domains with...
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Weak KAM Approach to First-Order Mean Field Games with State Constraints
We study the asymptotic behavior of solutions to the constrained MFG system as the time horizon T goes to infinity. For this purpose, we analyze...
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A Mean Field Game Model for Renewable Investment Under Long-Term Uncertainty and Risk Aversion
We consider a stylized model for investment into renewable power plants under long-term uncertainty. We model risk-averse agents facing heterogeneous...
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On the long time convergence of potential MFG
We look at the long time behavior of potential mean field games (briefly MFG) using some standard tools from weak KAM theory. Potential MFGs are...
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Approximation of Deterministic Mean Field Games with Control-Affine Dynamics
We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with...
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A Class of Optimal Control Problems of Forward–Backward Systems with Input Constraint
In this paper, we consider a new class of optimal control problems with admissibility constraint, where the state is driven by a fully coupled...
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A Coefficient Inverse Problem for the Mean Field Games System
A coefficient inverse problem (CIP) of the determination of a coefficient of the mean field games system (MFGS) of the second order is considered....
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Second order local minimal-time mean field games
The paper considers a forward–backward system of parabolic PDEs arising in a Mean Field Game (MFG) model where every agent controls the drift of a...
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Mean field games with state constraints: from mild to pointwise solutions of the PDE system
Mean Field Games with state constraints are differential games with infinitely many agents, each agent facing a constraint on his state. The aim of...
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Sharp semi-concavity in a non-autonomous control problem and \(\pmb {L^p}\) estimates in an optimal-exit MFG
This paper studies a mean field game inspired by crowd motion in which agents evolve in a compact domain and want to reach its boundary minimizing...
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Analysis of the Finite-State Ergodic Master Equation
Mean field games model equilibria in games with a continuum of players as limiting systems of symmetric n -player games with weak interaction between...
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On the Quadratic Convergence of Newton’s Method for Mean Field Games with Non-separable Hamiltonian
We analyze asymptotic convergence properties of Newton’s method for a class of evolutive Mean Field Games systems with non-separable Hamiltonian...
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Semi-linear parabolic equations on homogenous Lie groups arising from mean field games
The existence and the uniqueness of solutions to some semilinear parabolic equations on homogeneous Lie groups, namely, the Fokker–Planck equation...
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An Introduction to Mean Field Game Theory
These notes are an introduction to Mean Field Game (MFG) theory, which models differential games involving infinitely many interacting players. We...