Continuous time finite state mean field games
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In this article, a limiting mean field model is proposed for symmetric games where a large number of players can be in any one of d states and its main properties are characterized.Abstract:
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 limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study the $N+1$-player problem, which the mean field model attempts to approximate. Our main result is the convergence as $N\to \infty$ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.read more
Citations
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Mean Field Games Models—A Brief Survey
TL;DR: 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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A general characterization of the mean field limit for stochastic differential games
TL;DR: In this article, the mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon.
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On the existence of classical solutions for stationary extended mean field games
TL;DR: Gomes et al. as mentioned in this paper considered extended stationary mean-field games, which depend on the velocity field of the players, and established the existence of smooth solutions under fairly general conditions by applying the continuity method.
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On the connection between symmetric $N$-player games and mean field games
TL;DR: In this paper, the authors identify limit points of sequences of certain approximate Nash equilibria as solutions to mean field games for problems with Ito-type dynamics and costs over a finite time horizon.
References
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Mean Field Games
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Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$ -Nash Equilibria
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Markov Perfect Equilibrium: I. Observable Actions
Eric Maskin,Jean Tirole +1 more
TL;DR: This work defines Markov strategy and Markov perfect equilibrium and shows that an MPE is generically robust: if payoffs of a generic game are perturbed, there exists an almost Markovian equilibrium in the perturbed game near the initial MPE.