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Continuous Time Finite State Mean Field Games
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field…
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Discrete Time, Finite State Space Mean Field Games
In this paper we report on some recent results for mean field models in discrete time with a finite number of states. These models arise in situations that involve a very large number of agents…
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A stochastic analogue of Aubry-Mather theory
In this paper, we discuss a stochastic analogue of Aubry-Mather theory in which a deterministic control problem is replaced by a controlled diffusion. We prove the existence of a minimizing measure…
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Effective Hamiltonians and Averaging for Hamiltonian Dynamics I
Abstract: This paper, building upon ideas of Mather, Moser, Fathi, E and others, applies PDE (partial differential equation) methods to understand the structure of certain Hamiltonian flows. The main…
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Mean Field Games Models—A Brief Survey
TLDR
A brief survey of mean-field models as well as recent results and techniques is presented, and a definition of relaxed solution for mean- field games that allows to establish uniqueness under minimal regularity hypothesis is proposed.
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Two Numerical Approaches to Stationary Mean-Field Games
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization…
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Time-Dependent Mean-Field Games in the Subquadratic Case
In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain…
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Generalized Mather problem and selection principles for viscosity solutions and mather measures
Abstract In this paper we study the generalized Mather problem, whose applications range from classical mechanics to stochastic control and discrete dynamics, and present some applications to…
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Viscosity solution methods and the discrete Aubry-Mather problem
In this paper we study a discrete multi-dimensional version of Aubry-Mather theory using mostly tools from the theory of viscosity solutions. We set this problem as an infinite dimensional…
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A Mean-Field Game Approach to Price Formation
TLDR
This model is a constrained mean-field game (MFG) where the price is a Lagrange multiplier for the supply versus demand balance condition and the existence of a unique solution using a fixed-point argument is established.
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